Jan Hammer was born in Prague on April 17, 1948, when the city was the capital of Czechoslovakia. His mother, Vlasta Průchová, was a well-known Czech singer, and his father was a doctor who paid his way through school playing vibraphone and bass guitar. Hammer started piano at four, had formal lessons from six, and by fourteen was leading a jazz trio that played and recorded across Eastern Europe. At eighteen he was the pianist in violinist Stuff Smith's quartet at the 1966 Jazz Jamboree in Warsaw, with Kurt Lindgren on bass and Franco Manzecchi on drums, and the festival's releases credit him on "Perdido" and "Lady Be Good." He entered the Prague Academy of Musical Arts, where his coursework included harmony, counterpoint and classical composition.

The Warsaw Pact invasion of August 20, 1968 ended his studies. Ten days later he recorded a live trio set at the Domicile club in Munich with the bassist George Mraz, another young Czech musician who had left, and the drummer Cees See. MPS issued it as Malma Maliny (1969). He stayed in Munich long enough to play on the actress Kai Fischer's debut album, then took a scholarship at Berklee College of Music in Boston with the plan of becoming an American citizen, which he did in 1978. After Berklee he spent about a year as keyboardist and conductor with Sarah Vaughan, and he recorded with Elvin Jones and with the flutist Jeremy Steig before settling in New York. Steig's Energy (Capitol, 1971) has him on electric piano alongside Don Alias, Gene Perla and Eddie Gómez.

In 1971 he joined the original Mahavishnu Orchestra, which guitarist John McLaughlin built from violinist Jerry Goodman, bassist Rick Laird, Billy Cobham on drums and Hammer. He was found through a mutual friendship with Miroslav Vitouš of Weather Report. The band's The Inner Mounting Flame (1971) and Birds of Fire (1973, No. 15 on the Billboard 200) set the template for loud, fast, odd-metre jazz-rock, and Hammer was an early pioneer of playing a Minimoog live. The group played some 530 shows before its final concert on December 30, 1973; Hammer and Goodman had aired frustrations with McLaughlin's leadership in a magazine interview that year. Their last studio sessions, cut at Trident Studios in London in June 1973, stayed in the vault until The Lost Trident Sessions appeared in 1999. In the same year Hammer played piano and Moog on Cobham's debut Spectrum, including an unaccompanied piano piece, "To the Women in My Life."

Out of the band he made Like Children (Nemperor, 1974) with Goodman, then played organ, piano and synthesizer on guitarist John Abercrombie's ECM debut Timeless (1975) with Jack DeJohnette on drums, and keyboards on Stanley Clarke's second solo album (1974). His own The First Seven Days (1975) was recorded at Red Gate Studio, which he had built in a farmhouse in Kent, New York. It is a seven-part musical telling of the Genesis creation story, and the sleeve notes assure listeners that there is no guitar on it, even though some of the lead lines sound like one. The same studio hosted Elvin Jones Is "On the Mountain" (PM, 1975), on which Hammer plays acoustic and electric pianos and Moog, engineers, and wrote three tracks for the drummer's group with bassist Gene Perla.

The partnership that carried his name furthest in the 1970s was with the guitarist Jeff Beck. Hammer wrote "Blue Wind," plays synthesizer on four other tracks of Beck's platinum album Wired (Epic, 1976), produced by George Martin, and plays drums and keyboard bass on "Blue Wind" itself. A 117-date tour followed from June 1976 to February 1977, and it became Jeff Beck with the Jan Hammer Group Live (1977), which reached No. 23 on the Billboard 200 and went gold. The Jan Hammer Group, with Steve Kindler on violin, Fernando Saunders on bass and Tony Smith on drums, made Oh, Yeah? (1976) and Melodies (1977). Around them came Al Di Meola's Elegant Gypsy (1977), the albums Black Sheep (1978) and Hammer (1979), three pieces on Beck's There and Back (1980), the duo records Untold Passion (1981) and Here to Stay (1982) with Neal Schon of Santana and Journey, and the jazz-leaning Finger Dancing (1981), a co-billed album with the guitarist Yoshiaki Masuo on which Hammer wrote the first five tracks. He also plays on Tony Williams's The Joy of Flying (1979), where he is the keyboardist on four tracks, wrote three of them and engineered two.

In the fall of 1984 the producers of Miami Vice asked him to score the series every week. "Miami Vice Theme" was released as a single in 1985 and went to No. 1 on the Billboard Hot 100, the last instrumental to do so until Baauer's "Harlem Shake" in 2013, and the series soundtrack album spent 11 weeks at No. 1 on the Billboard 200 and sold more than four million copies in the United States. At the Grammy Awards in February 1986 the theme won both Best Pop Instrumental Performance and Best Instrumental Composition, and he had Emmy nominations in 1985 and 1986. He wrote the music for about 90 episodes and stepped back from the weekly schedule in 1988, keeping the theme in use to the end of the run. "Crockett's Theme," the slower piece from the show, became a European hit and was re-released in the UK in 1991, after a bank used it in a series of television commercials. He also wrote "Escape," which Beck recorded on Flash (1985) and which won Beck the 1986 Grammy for Best Rock Instrumental Performance.

Television and film took most of his time afterwards. He scored the British series Chancer (20 episodes), Vanishing Son, the film I Come in Peace, and from late 1993 through 2000 wrote the music for TV Nova, the first commercial television network in his native Czech Republic, which launched in February 1994. His computer-animation video album Beyond the Mind's Eye (1992) was one of the best-selling music videos on Billboard's chart in 1993. He still played with jazz musicians in this period, touring in the early 1990s with Tony Williams, including a July 4, 1991 set at the Montreal International Jazz Festival that was released on audio and video, and Drive (1994), his first album of new non-soundtrack material in several years, brought Beck and Michael Brecker back as guests. After a gap of more than a decade he released Seasons, Pt. 1 (2018), Sketches in Jazz (2020) and Seasons, Pt. 2 (2022), all on his own Red Gate label, and has since issued new versions of "Crockett's Theme" with the group The Second Sight, including one in 2023. His son Paul is a musician who has fronted the band Savoir Adore.

Hammer's playing came out of the Bill Evans, Erroll Garner and Paul Bley piano tradition and the Hammond organ of Jimmy Smith and Larry Young, and he has named the drummers Jo Jones, Philly Joe Jones, Elvin Jones and Tony Williams among his influences, two of whom he later recorded with. His own sound is something else: a keyboardist who treats the synthesizer as a lead voice and puts it in dialogue with a guitarist, McLaughlin in Mahavishnu, Beck on tour, Di Meola and Schon on record. The 1974 organ playing on Timeless is the closest he came to a conventional jazz-trio setting. The Rolling Stone Jazz Record Guide singled it out as some of the best organ playing he has recorded, and the Penguin Guide to Jazz called him underrated and credited him and Jack DeJohnette with giving the date its drive.

Most of his career lies outside that mainstream. His best-known work is television music, and his most widely heard recordings are a pop-chart instrumental, a rock guitarist's tour album and a run of soundtrack albums. Critics file the Mahavishnu Orchestra and his own groups under jazz fusion or jazz-rock, and he has described his own taste as sitting somewhere between experimental music and progressive rock. What ties the later screen work to the earlier jazz is method: he has said he scored Miami Vice on a Fairlight CMI sampler, sampling acoustic drums and percussion into it, and he made the music largely by himself in his own studio on a weekly deadline. The jazz side of his record is documented in the Prague trio, the 1966 Stuff Smith date, the Sarah Vaughan year, the Elvin Jones, Jeremy Steig, Charlie Mariano and Tony Williams sessions, an ECM album, and a 2020 solo album called Sketches in Jazz.