In 1984, aged 29, he was sold for a record fee of €5.7m to Inter Milan. Despite a notable beginning, in which he helped the team to compete until the end for the 1984–85 "Scudetto", Rumenigge's career in Italy was mostly marred by injury problems. At the end of his contract in 1987, Rummenigge moved on to Swiss first division club Servette FC in Geneva, where he saw his career out. In his last season, 1988–89, he had his last success, becoming top scorer in the Swiss league with 24 goals.