Heinrich Köbberling was born on 23 February 1967 in Arolsen, the small Hessian residence town now called Bad Arolsen. His first documented recording is a local one and it predates his professional career entirely: a Christmas cantata for young people by the composer Klaus Wüsthoff, cut with the choir, orchestra, wind players and rock band of the Christian-Rauch-Gymnasium in Arolsen, on which Köbberling plays drums. He went on to study percussion at the Hochschule für Musik und Theater in Hamburg and then at the Mannes College of Music, part of the New School in New York, and stayed on in the city for several years as a freelance player.

Those New York years produced his first working band and his first records as a leader. From late 1996 he co-led the trio PLK with the Australian saxophonist Lisa Parrott and the bassist Chris Lightcap, playing the Knitting Factory and other downtown rooms; the group issued Bab Bab on Goat Angel Records in December 1998 and toured Germany, including the Kassel International Jazz Festival. In 1997 he recorded his own quartet date Pisces for the German label Nabel with Matt Renzi on tenor saxophone, Ben Monder on guitar and Marc Johnson on bass. In November 1998 he cut the Derek Bronston Group's Longing in Brooklyn alongside Parrott and the bassist Gary Wang, and in September 1997 he had already made LeeAnn Ledgerwood's Now and Zen for SteepleChase. Back in Germany, the veteran altoist Herb Geller used him for I'll Be Back! (Hep, recorded in Hamburg in August 1996), and Gunter Hampel put him in his quartet for Time Is Now, taped live at the Eldena Jazz Festival on 3 July 1992.

The association that has defined his recorded output began around 2003, when he took over the drum chair in the Julia Hülsmann Trio. The handover is legible in the credits of the trio's Scattering Poems (ACT, 2003, with the Norwegian singer Rebekka Bakken): Köbberling plays five of the ten pieces and the outgoing Rainer Winch plays the other five. From Come Closer (Celebrating Randy Newman) in 2004 onward the chair is his alone, and the trio of Hülsmann, bassist Marc Muellbauer and Köbberling has held together ever since. It moved to ECM Records with The End of a Summer, recorded at Oslo's Rainbow Studio in March 2008 and produced by Manfred Eicher. Eight further ECM albums followed, the group expanding to a quartet with trumpeter Tom Arthurs for In Full View (2013) and A Clear Midnight (2015, with the singer Theo Bleckmann), then with saxophonist Uli Kempendorff from Not Far From Here (2019) through The Next Door (2022) and Under The Surface (2025). He is a writer for the band as well as its drummer: two of the twelve pieces on Imprint (2011) are his.

Alongside that he has held a second long-running chair, in the European edition of the Ernie Watts Quartet with pianist Christof Sänger and bassist Rudi Engel, documented from a Fulda club date in October 2003 (Alive) through Analog Man, Four Plus Four, Oasis, A Simple Truth, Wheel of Time and Home Light in 2018. His Berlin work runs in a sharply different direction: the Aki Takase groups Aki and the Good Boys and, with Alexander von Schlippenbach, the large-ensemble Eric Dolphy homage So Long, Eric!, recorded live in Berlin in June 2014, where he shares the drum chair with Han Bennink. He plays in the collective quartets Dok Wallach and Quartet Köcomabe, both of which include the bass clarinettist Rudi Mahall, and he has appeared well outside the idiom, on three albums by the Hamburg singer and rapper Jan Delay and on the dub-techno producer Moritz von Oswald's Dissent (2021) with Laurel Halo.

He is also a producer, most consistently for the Berlin singer Lyambiko, whose band he has drummed in since Inner Sense (2007); he shares the production credit on that record, on Something Like Reality (2010) and on Lyambiko Sings Gershwin (2012), and plays on all three.

His own leading has continued past the two records usually cited. Sonnenschirm (Jazzwerkstatt, recorded January 2009) put Rudi Mahall's bass clarinet against Tino Derado's accordion and piano and Paul Imm's bass; a third album under his own name, You and You, twelve original pieces on the Hamburg label schoener hören music, followed in May 2023. Alongside those he has co-led three collective quartets and, with the American pianist Larry Porter and the bassist Scott White, a trio that issued an archival Berlin concert from 2006 in September 2024 and a studio album, Reunion, in April 2026.

Teaching has run in parallel for more than two decades. He taught at the music academies in Hannover and Hamburg, then spent eighteen years at the Hochschule für Musik und Theater "Felix Mendelssohn Bartholdy" in Leipzig, where he became professor of jazz drums in 2007. In 2019 he left Leipzig for Berlin, taking up a professorship for jazz drums and ensemble at the Jazz-Institut Berlin, the joint jazz department of the Universität der Künste and the Hochschule für Musik Hanns Eisler, where he is also one of the artistic directors.

Köbberling's reputation rests on an unusual range rather than on a single signature. The ECM records with Julia Hülsmann ask for a quiet, elastic, colour-first approach in which the drums shade the piano's line rather than mark it, and that is the playing most listeners know; the Schlippenbach and Takase projects ask for the opposite, a dense free-jazz attack that can hold a fourteen-piece Dolphy ensemble together and share a bandstand with Han Bennink. Between those poles sits fifteen years of straight-ahead work in Ernie Watts's European quartet. Two worlds are audible in that spread: the Hamburg conservatory training, and the New York freelance years after his studies at the New School, which put him in downtown rooms with Chris Lightcap and Ben Monder before either was widely known. He writes as well as plays, contributing pieces to the Hülsmann trio's ECM albums and to Quartet Köcomabe, and his own leader dates favour unusual instrumentation over conventional rhythm-section formats: Sonnenschirm, recorded in January 2009, sets bass clarinet against accordion, piano and bass with no guitar or conventional comping.