The song was published by co-composer Lawrence Wright Music Co. London.
The first recorded version seems to be:
Arthur Briggs' Savoy Syncopators Orchestra 1927 (as "Souvenirs")
With Al Bowlly (vocals)
Recorded August, 1927 in Berlin
Labelliste von „Polydor (D)“ (1927-1928). Labelcode: 00309.
http://www.memorylane.org.uk/file/AB_Disco_S-Z.html
http://www.memorylane.org.uk/discography.htm
http://grammophon-platten.de/page.php?216.1
Released on (Deutsche) Grammophon 21122 and Polydor 211222
B-side of "Geh! Bubi (Do The Black Bottom With Me)"
Matrix 684bd; B-41884

Listen here:
4 months later Al Bowlly recorded another version in Berlin, this time with Fred Bird.
Fred Bird The Salon Symphonie Jazzband
(Fred Bird = Felix Lehmann) SEE: http://grammophon-platten.de/page.php?437
With Al Bowlly (vocals)
Recorded December, 1927 in Berlin
http://www.memorylane.org.uk/discography.htm
Released on Homocord Electro 4-2496
Matrix M-19749
Listen here:
Layton & Johnstone 1927
Recorded about Oct/Nov 1927 ?????
Released on Columbia 4533
Matrix A-6482
http://www.45worlds.com/78rpm/record/4533uk
https://www.discogs.com/Layton-Johnstone-Souvenirs-Charmaine/release/3498167

Listen here:
The version by The Kit-Cat Band was probably released after the version by Layton & Johnstone
But, according to the matrix-numbers, recorded before.
Untill now the version below by the Kit-Cat Band is considered as the very first recording.
THE KIT-CAT BAND directed by Al Starita
Al Starita-cl-as/dir. Tom Smith/Edwin Knight-t/Ted Heath-tb/Billy Ternent-as/George Smith-cl-ts/Eric Siday-Jean Pougnet-Vivian Dunn-vn/Harry Berly-vl/D. Cameron-vc/Sid Bright-p/Len Fillis-bj,g/Alfred Field-bb/Eric Little-d, -v, vocal Eddie Collis and Al Starita
Recorded Sept 19, 1927 Piccadilly Hotel Ballroom, London
Released on (British) Columbia 4563
Matrix A-6189-2
http://www.jabw.demon.co.uk/fillis.htm
https://www.discogs.com/The-Kit-Cat-Band-Paul-Ash-And-His-Orchestra-Souvenirs-Aint-That-A-Grand-And-Curious-Feeling/release/5422652
Listen here:
Within 1 month The Kit-Cat Band recorded another version, this time with Joe Leigh on vocals
THE KIT-CAT BAND directed by Al Starita
Piccadilly Hotel Ballroom, London, Oct 13, 1927
Al Starita-cl-as/dir. Tom Smith/Edwin Knight-t/Ted Heath-tb/Billy Ternent-as/George Smith-cl-ts/Eric Siday-Jean Pougnet-Vivian Dunn-vn/Harry Berly-vl/D. Cameron-vc/Sid Bright-p/Len Fillis-bj,g/Alfred Field-bb/Eric Little-d
WA-6189-3 Souvenirs

-v, vocal Joe Leigh MT-TMR
http://www.jabw.demon.co.uk/fillis.htm
Ronnie Munro's Orchestra 1927
Vocal trio
Recorded September 1927 in London
Released on Parlophone E-5901
Matrix E-1551-4 (Souvenirs)
Matrix E-1552-3 (Old Names Of Old Flames)
E-1551-3 features a vocal trio which may include Eddie Collis
Also released on Ariel 4250 (as ARIEL DANCE ORCHESTRA).
http://www.jabw.demon.co.uk/collis2.htm
http://www.turnipnet.com/mom/ronniemunro.htm
http://www.mgthomas.co.uk/Soundfiles/British%20Dance/British-Dance-Soundfiles.htm
The 3 subsequent Parlophone releases also contained a version of "Souvenirs" and "Old Names Of Old Flames".
Parlophone E-5902 The Singing Serenaders - Souvenirs
Parlophone E-5902 The Singing Serenaders - Old Names of Old Flames
Matrix E-1538-2 . Souvenirs
Matrix E-1539-2 . Old Names Of Old Flames
Given the matrix number (#1538-2), this could very well be the FIRST RECORDED version of "Souvenirs" (but the evidence has yet to pop up)

The same recording (matrix 1538-2) was also released on the Ariel-label (#4253)

Parlophone E-5903 Ronnie Munro and Barry Mills (Pianos) - Old Names of Old Flames
Parlophone E-5903 Ronnie Munro and Barry Mills (Pianos) - Souvenirs
Matrix E-1555-4 . Souvenirs
Matrix E-1556-4 . Old Names Of Old Flames

Parlophone E-5904 Frank Westfield's Orchestra - Souvenirs
Parlophone E-5904 Frank Westfield's Orchestra - Old Names of Old Flames
http://www.78rpmcommunity.com/beta/wiki/print-view/pageId/70
(c) Jack Hylton 1927 (as "Souvenirs")
Vocals Jack Jackson, Billy Ternent, Chappie d'Amato
Recorded September 21, 1927 in
Released on HMV B-5356
http://www.45worlds.com/78rpm/record/b5356
http://www.78source.co.uk/jack-hylton-orchestra-souvenirs-hmv-b5356-78-rpm.html
http://www.jackhylton.com/discography-1927-1930/
Listen here:
http://www.petefaint.co.uk/jackhylton/souvenirs.mp3
Len Fillis (guitar solo with Syd Bright at the piano)
Recorded October 21 21 1927 in London
Released on Columbia 4678
Matrix WA-6430-1
http://www.jabw.demon.co.uk/fillis.htm
The first US version seems to be:
Nick Lucas 1927
Recorded October 12, 1927 in New York
Released on Brunswick 3684
Matrix E24720/1
Listen here:
Astorites (= Fred Rich Orchestra)
Vocals Scrappy Lambert
Recorded October 21, 1927 in New York
Released on Harmony 528-D
http://adp.library.ucsb.edu/index.php/talent/detail/76086/Fred_Rich_Hotel_Astor_Orchestra_Musical_group
Listen here:
Also released on Diva 2528-G
https://www.discogs.com/Astorites-Brown-Morris-Orchestra-Among-My-Souvenirs-Rose-Of-Monterey/release/4544625
Ben Selvin 1927
Vocals: Cyril Pitts
Recorded October 24, 1927 in New York
Released on Columbia 1188-D
http://adp.library.ucsb.edu/index.php/objects/detail/195255/Columbia_1188-D
https://www.discogs.com/Ipana-Troubadours-Ben-Selvin-And-His-Orchestra-Dream-Kisses-Among-My-Souvenirs/release/4371812
Listen here:
Caroliners (= Sam Lanin Orchestra)
Vocal Scrappy Lambert
Recorded November 5, 1927 in New York
Released on Cameo 1258
and Lincoln 2723
https://www.discogs.com/Little-Club-Dance-OrchestraCaroliners-Kiss-of-Spring-Among-My-Souvenirs/release/7628055
and Romeo 492
https://www.discogs.com/The-Caroliners-Little-Club-Dance-Orchestra-Among-My-Souvenirs-Kiss-Of-Spring/release/4705597
Golden Gate Orchestra ( = California Ramblers) 1927
Vocal Ed Lloyd (= John Ryan)
Recorded November 18, 1927
Released on Perfect 14895 and on Perfect 36714
Matrix: 107913
Also released in the UK on Perfect P-315 (as by Meyer's Dance Orchestra)
“Souvenirs” is also issued on Pathe Actuelle 11508 as Casino Dance Orchestra. Some copies of P-315 use an American master by The California Ramblers. It is not know which masters are used on the PA issue.
http://mgthomas.co.uk/Records/LabelPages/Perfect-UK.htm
Listen here:
Regent Club Orchestra ( = Bob Haring Orhestra) 1927
Vocal: Lewis James
Recorded November 14, 1927 in New York
Released on Brunswick 3723
http://www.45worlds.com/78rpm/record/3723
Listen here:
Justin Ring's Okeh Orchestra (= Sam Lanin Orchestra)
Vocal Scrappy Lambert
Recorded November 21, 1927 in New York
Released on Okeh 40945
Listen here:
The Revelers - Among My Souvenirs (1927)
Recorded November 23, 1927 in New York
Released on Victor 21100

http://adp.library.ucsb.edu/index.php/matrix/detail/800015337/BVE-41106-Among_my_souvenirs
Listen here:
Roger Kahn 1927
Vocal: Scrappy Lambert
Recorded November 23, 1927
Released on Victor 21084
http://adp.library.ucsb.edu/index.php/matrix/detail/800015335/BVE-41104-Among_my_souvenirs
Listen here:
James Melton (1927)
Recorded December 14, 1927 in New York
Released on Columbia 1238-D
http://adp.library.ucsb.edu/index.php/matrix/detail/2000035122/145407-Among_my_souvenirs
https://www.discogs.com/James-Melton-Among-My-Souvenirs-Dear-On-A-Night-Like-This/release/7923577
Listen here:
Paul Whiteman and his Orchestra - Among My Souvenirs (1927)
Recorded November 22, 1927
Released on Victor 35877
https://www.discogs.com/Paul-Whiteman-And-His-Orchestra-Among-My-Souvenirs-Washboard-Blues/master/510439
http://adp.library.ucsb.edu/index.php/matrix/detail/800015165/CVE-40934-Among_my_souvenirs
Listen here:
http://www.jazz-on-line.com/a/mp3a/VIC35877.mp3
Markel's Society Favorites 1927
Vocal Irving Kaufman.
Recorded November 25, 1927 in New York
Released on Domino 4059
Also released on Banner 6121 (as by Gotham Society Orchestra)
http://www.45worlds.com/78rpm/record/6121us
Listen here
Abe Lyman 1927
Vocals Phil Neely
Recorded December 15, 1927
Released on Brunswick 3753
http://www.45worlds.com/78rpm/record/nc742307us
Listen here:
Orchestra Dobbri 1928 ( as "Ein bißchen Seligket") (German lyrics: Fritz Rotter)
Recorded in Berlin on February 18, 1928
Released on Parlophon B.7545
Listen here:
Irene Ambrus "Ein bißchen Seligkeit" ((German lyrics: Fritz Rotter)
Irene Ambrus (S), Otto Dobrindt (cnd), 'Lindström' (orch)
Recorded April 28, 1928 in Berlin
Released on Beka B 6426-II (mx. 34871)
http://www.truesoundtransfers.de/Titellisten/TT3082.htm
Listen here:
Comedian Harmonists - Ein bißchen Seligkeit - 1928
Recorded August 18, 1928 in Berlin
Released on Odeon O-2586 (matrix Be7120)
Listen here:
Jan Garber 1936
Vocal Lew Palmer
Recorded July 1, 1936 in Los Angeles
Released on Decca 1007

Benny Carter 1940
Recorded January 30, 1940
Released on Vocalion 5458
http://www.45worlds.com/78rpm/record/nc270706us
Listen here:
http://www.jazz-on-line.com/a/mp3d/OkeM-1126-1.mp3
Eddy Howard 1940
Recorded June 28, 1940 in Chicago
Released on Columbia 35949
http://www.honkingduck.com/discography/artist/eddy_howard
Louis Armstrong 1942
Louis Armstrong (tp, vcl), Frank Galbreath, Shelton Hemphill, Bernard Flood (tp), George Washington, James Whitney, Henderson Chambers (tb), Rupert Cole, Carl Frye (cl, as), Prince Robinson (cl, ts), Joe Garland (cl, ts, arr), Luis Russell (p), Lawrence Lucie (g), John Simmons (b), Sid Catlett (d), Sy Oliver (arr).
Recorded April 17, 1942 in Los Angeles
Released on Decca 4327A,
https://www.vmauctions.com/items/item_details.php?id=11086&ItemType=
Listen here:
http://incoming.jazz-on-line.com/a/mp3c/DECDLA2975.mp3
Etta Jones 1946
Etta Jones (vcl) acc by George Treadwell (tp) Dickie Harris (tb) Budd Johnson (ts) Jimmy Jones (p) Al McKibbon (b) J.C. Heard (d)
Recorded June 11, 1946 in New York
Released on RCA Victor 20-1998
http://www.45worlds.com/78rpm/record/201998
Listen here:
http://www.jazz-on-line.com/a/2016/CA499899.mp3
Frank Sinatra 1946
Recorded July 1946
Released on Columbia 37161
http://www.45worlds.com/78rpm/record/37161
https://www.discogs.com/Frank-Sinatra-Among-My-Souvenirs-September-Song/master/407405
Listen here:
Bing Crosby and Russ Morgan's Orchestra 1946
Recorded August 22, 1946,
Released on Decca 23745A,

Listen here:
Alvino Rey 1946
http://www.45worlds.com/78rpm/record/338
https://www.discogs.com/Alvino-Rey-And-His-Orchestra-Among-My-Souvenirs-Save-Your-Sorrow-For-Tomorrow/release/7771923
In 1946 Hoagy Carmichael plays the tune in a barscene in the movie "The Best Years Of Our Lives".
https://en.wikipedia.org/wiki/The_Best_Years_of_Our_Lives
Release dates November 21, 1946 (United States)
Watch it here at 3 min and 15 seconds in the next clip:
http://www.tcm.com/mediaroom/video/314754/Best-Years-Of-Our-Lives-The-Movie-Clip-Among-My-Souvenirs.html
Judy Garland 1957
http://www.45cat.com/record/eap1835us
In 1959, Connie Francis recorded the song peaking at number seven on the Hot 100.
The Connie Francis version also peaked at number ten on the R&B charts.
In the United Kingdom, the song reached #11.
https://www.discogs.com/Connie-Francis-Among-My-Souvenirs/master/766083
Listen here:
Imca Marina (1960) (as "In mijn herinnering") (Dutch lyrics: Dick Das)
Released on the B-side of Imperial HI 1024
https://nl.wikipedia.org/wiki/Imca_Marina
http://www.45cat.com/record/hi1024
In 1976, Marty Robbins had his 16th and last number one on the country charts with his version of the song.
http://www.45cat.com/record/310396
https://www.discogs.com/Marty-Robbins-Among-My-Souvenirs-Shes-Just-A-Drifter/master/638726
https://www.discogs.com/Marty-Robbins-El-Paso-City-Among-My-Souvenirs/release/4986123
More versions here:
https://secondhandsongs.com/work/89361/versions#nav-entity
http://www.originals.be/en/originals.php?id=186
http://nummer1hits.nl/?page_id=1313