Together with his husband Ivo van Hove, whom he met in 1980,[1][2] he created two theatre groups in the early 1980s: "Akt/Vertikaal" and "Toneelproducties De Tijd".
Versweyveld then started working as scenographer for the Zuidelijk Toneel in Eindhoven in 1990, with Ivo van Hove as the director of the company.
[3] In 2001 he became the head of scenography and the main designer for Toneelgroep Amsterdam.
[3] Versweyveld was also the set and lighting designer for Lazarus, the musical by David Bowie and Ivo van Hove, and for Network, the play by Lee Hall.
[2] In 2019 he was the scenographer for Camp: Notes on Fashion, the yearly Met Gala Exhibition at the Anna Wintour Costume Center.