Wilbur James "Jimmy" Cobb was born in Washington, D.C., on January 20, 1929, and bought his first drum set at thirteen with money saved from a busboy job. He took a short course of lessons from Jack Dennett, a percussionist with the National Symphony Orchestra, but was otherwise self-taught, learning by listening: he stayed up for the late-night broadcasts of the New York disc jockey Symphony Sid and worked out what he heard on the kit. His first professional jobs came around age eighteen, with saxophonist Charlie Rouse at Republic Gardens on U Street, and in the same Washington years he played behind Leo Parker, Benny Golson, Frank Wess, Pearl Bailey, and Billie Holiday.

He turned full-time touring musician in 1950 with the alto and tenor saxophonist Earl Bostic, whose band gave him his first recordings, and moved to New York at twenty-one. In 1951 he met Dinah Washington while on the road with Bostic; he joined her group, became her drummer and musical director for about three and a half years, and was her romantic partner during that stretch. He is on her 1955 EmArcy album For Those in Love, with arrangements by Quincy Jones. After leaving Washington's band he worked with Clark Terry and Dizzy Gillespie, then took the drum chair in the quintet Cannonball Adderley and his brother Nat had brought to New York, recording Cannonball's Sharpshooters for EmArcy in 1958.

Adderley's recommendation put him in the most famous band in jazz. Cobb replaced Philly Joe Jones in Miles Davis's sextet in May 1958 and stayed until early 1963, longer than any of the group's other members from that period. He plays on part of Porgy and Bess, the Gil Evans orchestral collaboration recorded in four sessions between July 22 and August 18, 1958, and on all of Kind of Blue, cut in two afternoons at Columbia's 30th Street Studio in New York: March 2, 1959 produced "So What," "Freddie Freeloader," and "Blue in Green," and April 22, 1959 produced "All Blues" and "Flamenco Sketches." The band was John Coltrane and Cannonball Adderley on saxophones, Bill Evans on piano (Wynton Kelly on "Freddie Freeloader"), Paul Chambers on bass, and Cobb. Columbia released it on August 17, 1959; it went on to become the best-selling jazz album ever made, and Cobb, who outlived everyone else in the studio, spent the last three decades of his life being asked about it. His recollection stayed consistently unglamorous. It was, he said, just another Miles Davis record date, though he added that the musicians knew at the time it was good. He also plays on Sketches of Spain (1960), Someday My Prince Will Come (recorded March 7, 20, and 21, 1961), the two Blackhawk live albums from San Francisco in April 1961, and the Carnegie Hall concert with Gil Evans's orchestra of May 19, 1961. Tony Williams took over the drum chair in 1963.

The freelance work Cobb did around the Davis job is nearly as substantial. He is on Wynton Kelly's Kelly Blue (Riverside, recorded February 19 and March 10, 1959) and on the Kelly, Chambers, Cobb rhythm section that backs John Coltrane through most of Coltrane Jazz, recorded for Atlantic on November 24 and December 2, 1959. The December 2 session also produced "Naima," the one track on Coltrane's Giant Steps that uses this trio rather than the album's other rhythm sections. A week earlier, on November 10, 1959, the same three men had backed Wayne Shorter and Lee Morgan on Shorter's Vee-Jay debut Introducing Wayne Shorter. On March 2, 1961, two years to the day after the first Kind of Blue session, Cobb played drums on Pepper Adams and Donald Byrd's co-led quintet date Out of This World for the small Warwick label, with Laymon Jackson on bass and a 20-year-old Herbie Hancock at the piano. It was Hancock's first appearance on a commercial recording.

When Kelly left Davis in March 1963, Cobb and Chambers went with him, and the Wynton Kelly Trio became a working band in its own right. It toured nationally, recorded Full View at Plaza Sound Studios in September 1966, backed Joe Henderson on a 1968 live date later issued as Straight, No Chaser, and worked with Kenny Burrell and J.J. Johnson. Its most celebrated association was with Wes Montgomery: the quintet album Full House, recorded live at Tsubo in Berkeley on June 25, 1962 with Johnny Griffin added on tenor, and Smokin' at the Half Note, drawn from a June 1965 run at the Half Note in New York plus a September 22, 1965 studio session, a record Pat Metheny has called the greatest jazz guitar album ever made. Chambers died in 1969 and the trio broke up; Kelly died in Toronto in April 1971 at thirty-nine. From 1970 to 1978 Cobb was Sarah Vaughan's drummer, an eight-year run covering trio, big band, and symphony settings, with Vaughan's 1973 Live in Japan his own favorite of the results.

Cobb spent the following two decades freelancing in New York before finally building a leader catalog of his own in his late sixties and seventies, mostly with a stable cast. Jimmy Cobb's Mob, with Richard Wyands on piano, Peter Bernstein on guitar, and John Webber on bass, made Only for the Pure at Heart (Fable, 1998) and Cobb's Groove (Milestone, 2003). A run of Chesky albums followed: 4 Generations of Miles (2002) with George Coleman, Mike Stern, and Ron Carter; West of 5th and New York Time, both recorded in January 2006; Cobb's Corner (2007) with Roy Hargrove and Peter Washington; and Jazz in the Key of Blue (2009). Branford Marsalis devoted a 2006 volume of the Marsalis Music Honors series to him. He was named an NEA Jazz Master in 2009, the same year he took his "Kind of Blue at 50" So What Band around the American and European festival circuit and the U.S. House of Representatives passed a resolution honoring him and the album's fiftieth anniversary. He taught and gave master classes at Stanford, the New School, the University of North Carolina at Greensboro, Florida State, and the Brooklyn-Queens Conservatory. He kept working into his late eighties, cutting The Original Mob (2014) and This I Dig of You (2019) for Smoke Sessions with Bernstein and Webber, and appearing at the New Mexico Jazz Festival in 2017. Cobb passed away of lung cancer at his Manhattan home on May 24, 2020, at 91, survived by his wife Eleana Tee Cobb and their two daughters.

Cobb named Max Roach as his primary model, along with Kenny Clarke, Shadow Wilson, and Sid Catlett, and later took things from Art Blakey and Philly Joe Jones; what he built from them was a style defined by what he left out. He was largely self-taught and explained his signature ride-cymbal beat as a solution to a shortage rather than an aesthetic choice: he had to put the time somewhere, so he concentrated on making it audible on the cymbal. The result is the sound most listeners know from Kind of Blue, brushes and mallets riding under Miles Davis and Bill Evans with almost no fills, the pulse carried on the cymbal and the hi-hat and the bass drum used sparingly for accents. Drummer Peter Erskine's summary is the one most often quoted: nobody has ever played better quarter notes than Jimmy Cobb. That combination of a rock-steady beat, an unusually good ear for dynamics behind singers, and a complete absence of showmanship made him the drummer bandleaders called when the point was the music rather than the drums, which is why his Discogs credit list runs past a thousand releases while his own name is on fewer than fifty of them.