Joris Teepe was born in 1962 in The Hague, Netherlands (no publicly documented birth month or day). He trained at the Conservatory of Amsterdam, graduating in 1991 with a master's degree from the Amsterdam School for the Arts, and plays left-handed. In 1992 he moved to New York City with, by his own later account, little more than his bass and a suitcase, and quickly found work in the city's jazz scene; multiple biographical sources describe him taking early lessons with Ron Carter around this time.

His recording career as a leader began the following year: on September 9, 1993, at East Side Sound Studios in New York, he cut Pay As You Earn, co-led with tenor saxophonist Don Braden and featuring trumpeter Tom Harrell, pianist Cyrus Chestnut, and drummer Carl Allen, released in 1994 on Mons Records. It was the start of a long-running partnership with Braden that continued across Bottom Line (1996), Speak Low (1997, with Italian pianist Dado Moroni), Seven Days A Week (1998, with Chris Potter, Randy Brecker, James Williams, and Tony Reedus), Firm Roots (1999, billed to the Joris Teepe Quartet), For Adults Only (recorded live at Smalls in November 1998, billed to the Joris Teepe Quintet, with David Hazeltine, Chris Potter, and Bruce Cox), and Going Dutch (2004, again with Braden, Randy Brecker, George Colligan, and Gene Jackson).

Around 2000, Teepe joined drummer Rashied Ali's working band, beginning a partnership that lasted the full nine years until Ali's death in August 2009. Discogs lists Teepe under the "Rashied Ali Quintet" group entity for a session recorded in mid-2001 at Ali's own Survival Studios featuring saxophonist Frank Lowe, pianist Andrew Bemkey, and trumpeter Jumaane Smith, issued only posthumously in 2025 as Sidewalks In Motion. The reconstituted quintet's best-documented work came from a February 17-18, 2005 session at Survival Studios with pianist Greg Murphy, tenor saxophonist Lawrence Clark, and Jumaane Smith, released as Judgment Day, Vol. 1 and Vol. 2 (2006); the same working group, with Josh Evans replacing Smith on trumpet, recorded Live In Europe at the Jazz Happening festival in Tampere, Finland on November 2, 2007. Ali also crossed back over onto Teepe's own turf as a guest on Teepe's big-band album We Take No Prisoners (Challenge Records, 2009), a large ensemble also featuring Braden and Josh Evans. After Ali's death, Teepe paid tribute directly with a leader date titled In The Spirit Of Rashied Ali (2018, recorded at the Prins Claus Conservatoire studio in Groningen), a quintet record with reedmen Michael Moore, Johannes Enders, and Wayne Escoffery, guitarist Freddie Bryant, and drummer John Betsch; it earned an Edison Award nomination, the Dutch record industry's equivalent of the Grammys, in 2019.

Teepe's other major institutional project has been educational and transatlantic. He became director of Jazz Studies at the Prins Claus Conservatoire in Groningen, Netherlands, where he founded the "New York Comes To Groningen" exchange, pairing his New York sideman network with Dutch students; the 2002 album Jazz In Jazz Out - New York Comes To Groningen documents an edition of the ensemble with drummer Ralph Peterson, trumpeter Brian Lynch, trombonist Conrad Herwig, and pianists David Berkman and Dena DeRose. He has also held teaching posts at Queens College, CUNY, and at the New Jersey Performing Arts Center, and has split his time between Groningen and Teaneck, New Jersey. In 2004 he was nominated for the Bird Award at the North Sea Jazz Festival, in the category for an artist deserving wider recognition.

Teepe has continued recording steadily into his fourth decade in New York: Workaholic (2015), Conversations (2016, again with Braden), Stream (2020, a European quartet date recorded in Cologne with drummer Billy Hart), When Will The Blues Leave (recorded June 2020 at the Bimhuis in Amsterdam with saxophonist Benjamin Herman and drummer John Engels, released 2021), Chemistry (2021, a second volume of duo-plus-drummer recordings with Braden, alternating drummers Jeff "Tain" Watts and Louis Hayes), Dutch Connection (2023, a duo record with pianist Rob van Bavel), and The American Dream Today (recorded October 2023 in New Jersey, released 2024, with saxophonists Adam Kolker and Marc Mommaas, pianist Leo Genovese, and drummer Matt Wilson). He remained an active performer and recording artist as of 2026, still leading his working groups and big band out of New York.

Teepe's catalog splits fairly evenly between two identities that rarely overlap in one player: a mainstream hard-bop and post-bop combo bassist, built around his decades-long partnership with saxophonist Don Braden and drawing on his design as one of relatively few Dutch musicians to establish a full-time career inside the New York scene, and a free-jazz specialist through his nine years as Rashied Ali's bassist of choice during the drummer's final working period. His arranging and composing (over 100 originals across sixteen-plus albums, plus arrangements of Duke Ellington, Billy Strayhorn, and John Coltrane material for big band) runs alongside his playing career, and he leads his own Joris Teepe Big Band as a conducting bassist. His teaching, first as head of Jazz Studies at the Prins Claus Conservatoire in Groningen and later at Queens College, has made him as much an institution-builder for the Dutch jazz scene's connection to New York as a performer in his own right, formalized through the "New York Comes To Groningen" exchange he founded.