Trio Accanto was formed as the result of a discussion between Marcus Weiss and Yukiko Sugawara in 1992. "It happened on the way home from the Witten Days for New Chamber Music in 1992. I talked a lot with Yukiko during the trip, and we came up with the idea for this combination of instruments. I was especially interested in having a fixed ensemble in order to play pieces a number of times, because at that time I was playing in larger ensembles where only a few pieces with saxophone occurred in the concerts and these programs were often just played once." The trio performed for the first time in 1994. Christian Dierstein was invited to be the percussionist after the first few concerts which had featured Edith Salmen-Weber in that role. The first concert with Christian Dierstein was at Donaueschingen in 1994. Nicolas Hodges took over the role of pianist in 2013, having known Dierstein and Weiss since 2000. He succeeded Yukiko Sugawara who had retired from the group after their performance of Aureliano Cattaneo's trio-concerto Blut with the SWR Sinfonieorchester Baden-Baden Freiburg under François-Xavier Roth at Donaueschingen in 2012. The first performance of the trio with Hodges took place on 1 November 2013 in Prague, at the Contempuls Festival, in a programme including works by Toshio Hosokawa, Jo Kondo, Brice Pauset and Hans Thomalla. Although the individual members are based in Basel, Stuttgart and Freiburg, the trio rehearses solely in Freiburg, which it considers its home. In addition to concerts, Trio Accanto has coached chamber music at Time of Music Festival, Viitasaari, and IMPULS Academy, Graz.
Trio Accanto has over the years made many studio recordings of new works, for radio. Several of these were collected onto two CDs, on Assai and on Zeitklang. The trio has released many other individual performances on other CDs.
Trio Accanto have in recent years begun recording the highlights of its repertoire for Wergo, in purpose-made studio recordings. The first of these, Funambules, was released in December 2016 and featured music by Georges Aperghis, Rolf Riehm, Johannes Schöllhorn and Stefan Prins, all pieces commissioned by the trio in the first year of Hodges' membership. The second, Songs and Poems, was released in April 2018 and features music by Aldo Clementi, Andreas Dohmen, Wolfgang Rihm, Hans Thomalla and Walter Zimmermann, all of which are major works from the Trio's "old repertoire" which were not recorded by the Trio in earlier decades. The third CD, Other Stories was released in April 2020, and includes four previously unrecorded works by Helmut Lachenmann - two versions of Sakura Variations for trio, plus the solo piano versions of Marche Fatale and Berliner Kirschblüten - along with trio works by Michael Finnissy, Yu Kuwabara, Martin Schüttler and Martin Smolka. A fourth CD has been recorded, solely consisting of works by Christian Wolff, including Trio IX - Accanto and recent Exercises. With Hodges, the Trio has also released a recording of a work by Marina Khorkova.