Durante la década de 1950, toca con su propio cuarteto, dentro de la escena del West Coast jazz, incorporándose en 1961 a la big band de Gerald Wilson, dedicándose a partir de entonces, con preferencia, a la composición y los arreglos. A partir de los años 1980, colabora asiduamente con el cantanteTom Waits.
Discografía
Como líder/colíder
1947 The Foremost! – con Dexter Gordon (Onyx #201; con Leo Parker y Wardell Gray)
1948 Central Avenue Breakdown, Vol. 1 (Onyx #212; con Vivien Garry/Arv Garrison y Dodo Marmarosa)
1949 Central Avenue Breakdown, Vol. 2 (Onyx #215; con Barney Kessel y Slim Gaillard)
1959 At Falcon's Lair – con Joe Castro (Metrojazz; con Sonny Rollins: At Music Inn)
1959 It's About Time – con Les McCann (Pacific Jazz)
1960 Sunset Eyes (Pacific Jazz; reissued on Blue Note)
1960 Teddy's Ready! (Contemporary; reissued on OJC)
1960 Back to Avalon (Contemporary)
1961 Together Again!!!! – con Howard McGhee (Contemporary; reissued on OJC)
1961 Good Gravy! (Contemporary; reissued on OJC)
1962 Heart & Soul (Contemporary; reissued on OJC)
1966 Nothin' But the Truth! (Prestige; reissued on OJC)
1967 It's All Right! (Prestige; reissued on OJC)
1974 Feelin's (Muse)
1976 The Inimitable Teddy Edwards (Xanadu)
1978 Young at Heart (Storyville) con Howard McGhee
1978 Wise in Time (Storyville) con Howard McGhee
1980 Out of This World (SteepleChase)
1981 Good Gravy [live] (Timeless)
1991 Mississippi Lad – con Tom Waits (Antilles)
1993 Blue Saxophone (Verve)
1994 La Villa: Live in Paris (Verve)
1994 Horn to Horn – con Houston Person (Muse; reissued on Savoy)
1995 Tango in Harlem (Verve)
1997 Midnight Creeper (HighNote)
1999 Close Encounters – con Houston Person (HighNote)
2001 Ladies Man (HighNote)
2003 Smooth Sailing – con Richard Wyands, Ray Drummond, Chip White (HighNote)