Tony Oladipo Allen was born on July 20, 1940, in Lagos, the son of James Alabi Allen, a motor mechanic from Nigeria, and Prudentia Mettle, who came from the Gold Coast (now Ghana). He trained as an engineer and was working at a Lagos radio station when, at 18, he taught himself to play drums. Around him were juju, the growing highlife scene of Nigeria and Ghana, and the American jazz records he studied closely, especially those of Art Blakey, Max Roach and Philly Joe Jones, along with the Ghanaian drummer Guy Warren, later known as Kofi Ghanaba, who had pioneered an Afro-jazz fusion. Sir Victor Olaiya hired him to play claves with his highlife band, the Cool Cats, and Allen moved to the drum chair when the group's drummer left. He went on to play with Agu Norris and the Heatwaves, the Nigerian Messengers, and the Melody Makers.

In 1964 Fela Kuti invited him to audition for a jazz-highlife band he was forming, and Allen became an original member of Koola Lobitos; Kuti, who had heard him on the Lagos circuit, asked how it was that he was the only drummer in Nigeria playing a mixture of jazz and highlife. After the group's 1969 trip to the United States it became Africa '70, with Allen as musical director, and its sound, built from soul and funk grooves, jazz, highlife and Yoruba polyrhythm, was named Afrobeat. Kuti wrote out parts for the other players, but Allen originated his own drum patterns, and Kuti later said that without him there would be no Afrobeat. Allen recorded more than 30 albums with Kuti. Tension over royalties and credit grew through the 1970s; Kuti supported three Allen solo records, Jealousy (1975), Progress (1977) and No Accommodation for Lagos (1979), but in 1979 Allen left Africa '70, and many of its members left with him.

He formed his own group, the Afro Messengers, recorded No Discrimination, and played in Lagos until he moved to London in 1984. A year later he settled in Paris, where he lived for the rest of his life and eventually took French citizenship. In London he made N.E.P.A. (Never Expect Power Always) with his band Afrobeat 2000, and in Europe he worked as a session drummer for King Sunny Adé, Ray Lema and Manu Dibango. After a quiet stretch he returned in the late 1990s with a run of singles and then Black Voices (1999), produced by the DJ Doctor L, which carried Afrobeat toward dub and electronic music; HomeCooking followed in 2002 with Damon Albarn among the guests. Lagos No Shaking (2006) was recorded live in Lagos with a full Afrobeat band and marked a return to the older sound.

Albarn had name-checked him in Blur's 2000 single "Music Is My Radar," and Allen got in touch with him after hearing it. In 2006 he joined Albarn, Paul Simonon of the Clash and Simon Tong of the Verve in The Good, the Bad & the Queen, whose self-titled debut appeared in 2007 and whose second album, Merrie Land, followed in 2018. With Albarn and the Red Hot Chili Peppers bassist Flea he made the 2012 album Rocket Juice & the Moon. His own albums in these years included Secret Agent (2009, World Circuit) and Inspiration Information 4 (2009) with the Finnish musician Jimi Tenor, and in 2014 he made Film of Life for the Jazz Village label with the French trio the Jazz Bastards, which AllMusic reports reached the top five of the World Music Albums chart.

Late in his career he turned back to jazz repertoire. In 2017 Blue Note issued his four-track EP A Tribute to Art Blakey & the Jazz Messengers, which reworks Bobby Timmons's "Moanin'" and Dizzy Gillespie's "A Night in Tunisia" for his French seven-piece band, and then the full-length The Source (September 2017), written with the saxophonist Yann Jankielewicz, who served as musical director, for a horn-and-keyboards band with Albarn on piano for one track. His final studio album in his lifetime was Rejoice (World Circuit, March 20, 2020), a set of originals by Allen and Hugh Masekela that producer Nick Gold had first recorded in London in 2010; after Masekela died in 2018, Allen and Gold finished the album in 2019 with younger London players including Joe Armon-Jones, Tom Herbert, Mutale Chashi and Steve Williamson. A documentary about his life, Birth of Afrobeat, reached American public television in January 2020, and in March 2020 he played on the Gorillaz track "How Far?" with Skepta.

Allen passed away on April 30, 2020, at the Georges Pompidou European Hospital in Paris, of an abdominal aortic aneurysm, at 79. Albarn called him his number one musical teacher, and Brian Eno had described him as perhaps the greatest drummer who ever lived. Blue Note released a posthumous album, There Is No End, in 2021, built on drum tracks he recorded in 2019 and completed by producers Vincent Taeger and Vincent Taurelle with guests including Danny Brown and Sampa the Great. Further posthumous releases include The Solution Is Restless (2021), recorded in one night in November 2019 with Joan As Police Woman and Dave Okumu, Tony Allen JID018 (2023), made with Adrian Younge for the Jazz Is Dead series, and the EP Lagos Paris London (2024) with Foals singer Yannis Philippakis.

Allen's drumming rests on the independence of all four limbs: he could hold a pulse on the kick drum, accent it on the hi-hat and layer cross-rhythms on snare and cowbell, so that he sounded like several players at once; Kuti said he sounded like four drummers, and after Allen left Africa '70, Kuti reportedly needed four drummers to cover his parts. He worked from Art Blakey and Max Roach, who showed him how African rhythmic ideas could be applied to the drum set, and from the polyrhythms of Yoruba and highlife music, but insisted that his patterns were his own. The result, the Afrobeat beat, was shaped with Fela Kuti and has been called the rhythmic core of the style. Most of his catalog is Afrobeat, Afro-funk and electronic-leaning world music rather than jazz in the narrow sense, and AllMusic files him under International and R&B; the jazz strand is real but concentrated in his early Koola Lobitos years and in his late Blue Note work, where critics wrote that The Source balances his jazz and Afrobeat sides, with modal workouts and horn arrangements beside the funk grooves. Because of that, only the two closest jazz subgenres are tagged. He influenced a generation of drummers and producers, among them Damon Albarn, Flea and Brian Eno, and his late projects with Hugh Masekela, Adrian Younge and a younger London jazz scene connected him to the new generation of jazz musicians.