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.

Another major part of Wohlert's work was on Danish churches. He thus designed Stengård Church and worked on the restoration of both the Lutheran and Catholic cathedrals of Copenhagen: the Church of Our Lady and St. Ansgar's Church. He also designed the mausoleum of King Frederick IX at Roskilde Cathedral.

He also built a number of houses - complete with his own furniture and furnishings - that provide an exemplar of the Danish vision of modern domestic architecture. These include a group of linked courtyard-like houses at Piniehoj, north of Copenhagen; built-in white-painted brick and timber, they are akin to a domesticated Louisiana.

Wohlert was also an educator, early in his career at University of California, Berkeley, and later for many years as a professor at the Royal Danish Academy of Fine Arts.