Benny's musical background came from his father and grandfather; both enjoyed playing the accordion. At the age of six Benny got an accordion of his own. Father Gösta and grandfather Efraim taught him Swedish folk music. When he was ten he had one or two piano lessons but found it rather boring. He left school at the age of fifteen and began to perform at youth clubs. This is when he met his first girlfriend Christina Grönvall. They never got married but did have two children: Peter in 1963 and Helen in 1965.

In 1964 Benny became the keyboard player of the rock 'n roll group Hep Stars. In 1965 Benny started to write material for the band, such as the number one hit Sunny Girl.

In the summer of 1969 Benny met Anni-Frid Lyngstad at the same time as Björn Ulvaeus met Agnetha Fältskog. Benny was engaged to Anni-Frid for about 9 year. They married in 1978 but got divorced in 1981. The personal relationships and Benny and Björn's composition has led quite naturally to the very close co-operation which the four friends have had during the previous two years.

After being a member of Hep Stars and later ABBA he has created the musicals Chess, Kristina från Duvemåla (based on the Immigrant novels by Swedish writer Vilhelm Moberg) (currently in workshops for an English production on Broadway), and Mamma Mia! (based on existing ABBA songs), all of these together with Björn Ulvaeus.

Andersson believes folk music to be an essential heritage of any nation which must be kept alive and continuously developed, and to that end he performs folk music on the accordion together with Orsa Spelmän. Since the late nineties he mostly plays with his band Benny Anderssons orkester (Benny Andersson's orchestra/band) with Helen Sjöholm from Kristina from Duvemåla on vocals.