Wohlert was educated at the Royal Danish Academy of Fine Arts' School of Architecture, where one of his teachers was Kaare Klint. In 1958 he and his partner Jørgen Bo started work on the Louisiana Museum of Modern Art, a project on which they would work for the next 33 years. They were also responsible for the Bochum Museum of Art, as well as the Gustav Lübcke Museum in Hamm, both in Germany.