The ensemble was established in June 2018 by students of the Hochschule für Musik und Tanz aus Köln and was named after the French 18th century folk-dance Réjouissance, which would be one of the movements of a suite. This title could be translated as "happiness".
The basic formation of La Réjouissance is Traverso, Viola da Gamba/Baroque Violoncello and Harpsichord.
Nevertheless, in their aim of approaching as much repertoire as possible, they also perform as bigger ensembles.
In July 2019, the trio became scholar of the Werner Richard - Dr. Carl Dörken Stiftung.