Born in Virum, he started playing football at nearby 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 secondary Danish 2nd Division league. Berggreen was Lyngby's top goalscorer in several seasons, and scored 15 goals when the club won promotion for the top-flight Danish 1st Division in 1979. He made his Danish national team debut in August 1979, in the first game of newly appointed national manager Sepp Piontek. He played one more national team game, 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 championship. Berggreen helped the club stay in the Serie A, and was recalled to the Danish national team in October 1982. In the 1983-84 Serie A season, Pisa were relegated into the 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 injury time, as Denmark were eliminated on penalty shootout. He helped Pisa win the 1985 Serie B series, to reenter the Serie A championship. Pisa were relegated once more at the end of the 1985-86 Serie A season. For the 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 Norway by 0-1 at half-time. Ten minutes after the break, Berggreen snapped the ball from a Norwegian defender, and made the assist as Michael Laudrup equalised 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 main tournament, 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 AS Roma. He played a single season at Roma, which ended in a seventh place in the 1986-87 Serie A. He moved on to league rivals Torino Calcio, whom he helped finish in sixth place the next 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 national team 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, 32 years old, 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 clothes company.
