Ensemble Adapter was founded by Matthias Engler and Gunnhildur Einarsdóttir in 2004. From its foundation Matthias Engler has been the ensemble's artistic director and manager. Ensemble Adapter's early years were shaped by a close collaboration with the Berlin composers collective Klangnetz e.V. (2004-2007). The group first appeared in a flexible size, with varying instrumentation built around percussion and harp.

In the following years (2007-2012) the group increasingly solidified into a steady quintet setting with Kristjana Helgadóttir (flute), Ingólfur Vilhjálmsson (clarinet), Gunnhildur Einarsdóttir (harp), Marc Tritschler (piano) and Matthias Engler (percussion) – paying tribute to Toru Takemitsu's ensemble Sound Space Ark and its forgotten repertoire from the 1970s and 80s in Japan. From 2012 to 2022 Helgadóttir, Vilhjálmsson, Einarsdóttir and Engler carried on as a quartet, with selected guest instrumentalists occasionally expanding the ensemble with as many as ten musicians.

Since 2022 Gunnhildur Einarsdóttir and Matthias Engler have been leading the group as an artistic team, without being bound to a specific instrumentation. With changing collaborators on a project-by-project basis, the focus lies on the creation of original artistic content, both in music and across all art forms.