Andersson was engaged to Anni-Frid Lyngstad of ABBA for about nine years. They married in October 1978, but divorced in 1981.
In February 1969, Lyngstad met Benny Andersson, and the couple were engaged in August 1969. By 1971 they were living together, but did not marry until 6 October 1978, during the height of ABBA's success.
However, after only three years of marriage, they separated in February 1981 and were divorced in November of the same year.