Olsen won the 1981–82 Eredivisie championship in his first season at the club (117 goals for and 42 goals against). The next season, 1982–83, Ajax successfully defended the Eredivisie title, and also won the Dutch Cup to complete The Double, with also young players Jan Molby and Marco van Basten in the squad. In the 1983-84 season, Olsen was the best player in the match Ajax-Feyenoord (8-2!). Olsen scored twice in the qualification tournament for Euro 1984, including a last-minute equaliser in the 2–2 draw against England. He was selected to represent Denmark at the finals tournament, and played two games, including Denmark's semi-final against Spain. The game ended a draw, but even though Olsen scored in the penalty shootout, Denmark were eliminated when Preben Elkjær missed his shot.