Kenny Washington was born May 29, 1958, in Staten Island, New York, and grew up in the Stapleton Houses, attending P.S. 14 before studying at the High School of Music & Art, from which he graduated in 1976. He is the brother of bassist Reggie Washington. Washington studied privately with Rudy Collins, a former drummer for Dizzy Gillespie, and was working professionally while still a teenager: he recorded with Lee Konitz's nonet in 1977, a session issued on Chiaroscuro as Lee Konitz Nonet, alongside trombonist Jimmy Knepper and baritone saxophonist Ronnie Cuber.

Washington emerged in the late 1970s as one of a generation of young, bebop-schooled drummers whom older, established musicians sought out specifically for their command of the tradition. He worked with vocalist Betty Carter from 1978 to 1979, appearing on The Audience with Betty Carter, a live two-LP set recorded at San Francisco's Great American Music Hall in December 1979 and issued in 1980 on Carter's own Bet-Car label with pianist John Hicks and bassist Curtis Lundy; the record is widely considered her definitive live document. From 1980 he worked with tenor saxophonist Johnny Griffin, recording Call It Whachawana (1983, Galaxy) and, later, The Cat (1991, Antilles). The same period produced a recurring cooperative trio with pianist Ronnie Mathews: Song for Leslie, cut in Bologna, Italy on March 1, 1980 for the Red Record label with bassist Ray Drummond, billed jointly to all three musicians on the cover. Washington also worked in Europe during these years, recording Steve Houben & Michel Herr Meet Curtis Lundy & Kenny Washington (1983, Jazz Cats) with the Belgian reedman and pianist.

Through the 1990s Washington became one of the most heavily recorded drummers in mainstream, straight-ahead jazz, anchoring an enormous run of sessions for the Dutch label Criss Cross Jazz and its New York-based contemporaries. He was the house drummer behind pianist Mike LeDonne's early leader dates, including Common Ground (1992), and behind pianist Richard Wyands's four Criss Cross and Venus trio albums with bassist Peter Washington (no relation), beginning with Reunited (1995). He became baritone saxophonist Gary Smulyan's regular drummer starting with Smulyan's leader debut, The Lure of Beauty (1991), and returned across five of Smulyan's albums over the following two decades, through Smul's Paradise (2012). He reunited with Ronnie Mathews and a new bassist, Buster Williams, for the all-Thelonious-Monk program Shades of Monk (recorded in Japan, May 1994, released 1995), and recorded with alto saxophonist Lou Donaldson on Caracas (1994, Milestone) alongside organist Dr. Lonnie Smith and guitarist Peter Bernstein. He also appeared on tenor saxophonists Teddy Edwards and Houston Person's Close Encounters (recorded 1994, released 1999 on HighNote) and, in 1993, shared the drum chair on tenor saxophonist Joshua Redman's Grammy-nominated self-titled debut for Warner Bros., where he taught, and briefly co-anchored the rhythm section alongside, his own former drum student Gregory Hutchinson.

Since 1997 Washington has held the drum chair in pianist Bill Charlap's trio, alongside bassist Peter Washington, a partnership that has run close to three decades and produced a long run of Blue Note and Impulse! recordings, several of them Grammy-nominated, including Plays George Gershwin: The American Soul (2005) and Notes from New York (2016). Washington is also a widely respected jazz historian and discographer, with essays and liner notes for classic jazz reissues, including material by Art Blakey and Count Basie, and he serves on the faculty of both SUNY Purchase and the Juilliard School, in addition to an earlier stint teaching at the New School and working as an on-air announcer for the Newark jazz station WBGO.

Washington's more recent work spans both the tradition's elder generation and its newest star. He appears on Hank Jones Trio !!!, an archival trio recording with pianist Hank Jones and bassist George Mraz released by the Italian label Red Record in 2023, thirteen years after Jones's death, and on the cooperative session Second Wind (2024, Cellar Music), where his cover billing alongside pianist John Lee and bassist Peter Washington sits atop what reviewers confirm is Lee's own sophomore leader date. In 2023 he took the drum chair in the Heavy Hitters, the Mike LeDonne-led sextet with saxophonists Eric Alexander and Vincent Herring and trumpeter Jeremy Pelt, documented on the live album That's What's Up (2024, Cellar Music). Washington has also become a fixture on vocalist Samara Joy's recordings since her 2021 self-titled debut, including her Grammy Award-winning 2022 breakthrough Linger Awhile and the 2023 holiday album A Joyful Holiday.

Washington plays in the direct lineage of the bebop and hard-bop drummers he has spent a parallel career researching and writing about: Kenny Clarke, Max Roach, Philly Joe Jones, and Art Blakey. His time feel is precise, propulsive, and deeply idiomatic, and colleagues and critics alike have repeatedly singled out the breadth of his knowledge of the jazz tradition as what makes him such a reliable first-call sideman: a JazzTimes profile paired him with bassist Peter Washington as the defining mainstream-jazz rhythm section of their generation, prized less for reinventing the music than for playing it, night after night, exactly right. That same historical grounding drives his second career as a jazz historian, and it shows in his choice of collaborators, who span from bebop-era survivors like Tommy Flanagan and Hank Jones to the current generation's brightest new vocal star.