Born in
Kongens Lyngby, Berggreen started playing football at local club
Lyngby Boldklub at the age of six. He made his senior debut in 1975, in a Lyngby team which struggled to establish itself in the
Danish 2nd Division. Berggreen was Lyngby's top goalscorer for several seasons, and scored 15 goals when the club won
promotion to the
Danish 1st Division in 1979. He made his international debut for
Denmark in August 1979, in the first game of the newly appointed national manager
Sepp Piontek. He played one more game for his country, before his international career went on a hiatus. In 1982, he moved abroad to play for newly promoted club
SC Pisa in the Italian
Serie A. Berggreen helped the club stay in Serie A, and was recalled to the Danish national team in October 1982. In the
1983–84 Serie A season, Pisa were
relegated to
Serie B, but Berggreen chose to stay with the club. He was selected to compete for the Danish national team at the
1984 European Championship, where he played four matches, and scored a goal in the 5–0 victory against
Yugoslavia. In the semi-final against
Spain, Berggreen was
sent off in
extra time, and Denmark were later eliminated following
penalty shootout. The following season, he helped Pisa win the 1984–85 Serie B title, and obtain promotion to Serie A once again. Pisa were relegated once more at the end of the
1985–86 Serie A season. With the Danish national team, Berggreen played an important part in Denmark's first ever qualification for a
World Cup tournament. In the penultimate match of the
qualification stage in October 1985, Denmark were trailing against
Norway by 0–1 at
half-time. Ten minutes after the break, Berggreen snapped the ball from a Norwegian
defender, and made the assist for
Michael Laudrup to tie the game. Berggreen himself went on to score two goals, as Denmark eventually won 5–1. He was included in the Danish squad for the
1986 World Cup, and played three games, before Denmark were once again eliminated by Spain. After the World Cup, Berggreen opted to stay in the Serie A, and signed with vice-champions
A.S. Roma. He played a single season at Roma, which ended in a seventh-place finish in
Serie A. He then moved on to league rivals
Torino, whom he helped to finish in sixth place the following season. He was selected to represent Denmark at the
1988 European Championship in June 1988, where he played two games as a substitute. Berggreen ended his national career after the tournament, having played 46 matches and scored five goals since his international debut in 1979. Berggreen moved back to Denmark, where he ended his career with Lyngby, in a combined role as both active player and Lyngby sports director. He ended his active career in March 1990, at the age of 32 years, after more than 200 games for Lyngby. Lyngby struggled financially, and Berggreen left his job as a sports director in November 1992. He went on to concentrate on his clothing company. ==Honours==