In 1980–81 season, he went abroad for the first time in his career. That season he played for the Italian team Reyer Venezia. After just one season, he returned to his former club Partizan for one season. In the following seasons, he played for numerous European teams, including: Real Madrid, Reyer Venezia and Glaxo Verona. He finished his professional career in 1990–91 season, playing for Partizan's arch rivals Red Star Belgrade.
Dalipagić finished high school at the Technical School in Mostar, and graduated from the Teachers College in Belgrade. He is married to Sonja Požeg, former Yugoslav tennis player. They have two children, Sanja and Davorin.