Borgmann began his career in the early 1980s, working mainly with the Berlin Art Ensemble around Nick Steinhaus (participating in the 1981 Tour Southamerica for the Goethe-Institut, and the 1982 Nickelsdorfer Konfrontationen). He went on to the Sirone Sextet in New York (1987); the Hidden Quartet (with Dietmar Diesner, Erik Balke, and Jonas Akerblom); and Noise & Toys (with Valery Dudkin, Sascha Kondraschkin). In 1991, Borgmann founded the Orkestra Kith’N Kin (with Hans Reichel, John Tchicai, Pat Thomas, Jay Oliver, Mark Sanders, Lol Coxhill and others). Later he toured with his Quartet Ruf der Heimat (founded in 1993 with Ernst-Ludwig Petrowsky, Peter Brötzmann, Willi Kellers, Christoph Winckel), and with the Trio Blue Zoo (with Borah Bergman and Brötzmann). Starting in 1984, and continuing until 1996, he organized the festival STAKKATO in Berlin.
In 1995, Borgmann began working with Wilber Morris and Denis Charles, leading to the BMC-Trio. After Charles' death in 1998, Borgmann and Morris teamed with Reggie Nicholson in the BMN-Trio, which continued performing until 2002. Borgmann also participated in the quartet Alliance with Petrowsky, DJ jayrope and Michael Griener.
Initially with Tony Buck and Joe Williamson, Borgmann formed the trio Boom Box. He continues to perform with the group, now playing with Willi Kellers and Akira Ando. He also continues to tour international Jazz festivals around the world.