Andrésen had only appeared in one film, En kärlekshistoria (1970) at the time he was cast in Death in Venice, which gained him international recognition. While the film performed relatively poorly at the box office, Andrésen was noted for his performance as Tadzio, the beautiful young Polish boy with whom the film's older protagonist Gustav von Aschenbach (played by Dirk Bogarde) becomes obsessed. Film Historian Lawrence J. Quirk commented in his study The Great Romantic Films (1974) that some shots of Andrésen "could be extracted from the frame and hung on the walls of the Louvre or the Vatican."

Andrésen resides in Stockholm with his wife, poet Suzanna, and their daughter Robine. The couple had another child, a boy (their first child), who died of the Sudden Infant Death Syndrome in 1986, which caused the couple's temporary separation.

Eager to dispel the rumors regarding his sexuality and to shed his "pretty boy" image, Andrésen thereafter avoided homosexual roles and parts which he felt would play off of his good looks, and was angry when feminist Writer Germaine Greer used a photograph of him on the cover of her book The Beautiful Boy (2003) without his permission. Although Greer did consult Photographer David Bailey (who owned the copyright for the image) before publishing the book, Andrésen maintained that it is Common practice when a party uses an image of a person which has been copyrighted by a different individual to inform the individual and that he would not have given his consent for Greer to use his picture if she had informed him of her plans.

Andrésen has also appeared in several other films. These include Pelikaanimies (2004), Kojan (1992) and Smugglarkungen (1985).