Jesper Thilo was born on Christianshavn in Copenhagen in 1941 to a pianist-actress mother and a father who was an architect.[2] He started to play clarinet at age 11 and from 1955 to 1960 he played clarinet and trombone in various amateur Dixieland jazz bands with occasional paid jobs as a musician. Early he knew that he wanted to become a professional jazz musician but to get an education he chose to study classical clarinet at the Royal Danish Academy of Music[3]
While still a student at the Academy, Thilo joined Arnved Meyer's orchestra where he played from 1960 to 1964 and again from 1967 to 1974 and it was Arnved Meyer who convinced him to shift to saxophone. In Meyer's band he played with musicians such as Ben Webster, Benny Carter, Harry Edison, Roy Eldridge and Coleman Hawkins.[4] During this part of his career his virile Swing style chiefly inspired by Webster and Hawkins.[3] Besides his engagement in Meyer's orchestra, Thilo also played in his own band, a quintet which he had founded in 1965 and co-lead with Torolf Mølgaard and Bjarne Rostvold.
In 1989, he left the DR Big Band and Ernie Wilkins's orchestra to lead his own bands with members such as Søren Kristiansen, Olivier Antunes, Hugo Rasmussen og Svend-Erik Nørregaard.