Born in Örebro, Sweden, Brunkert began playing the drums in 1958 and cited jazz drummer Gene Krupa as a significant early influence.
He then formed the jazz-rock combo Opus III [sv] with the guitarist Janne Schaffer, and by 1970 had become one of the most sought-after session drummers in Stockholm.
[3] He was not among the four members of ABBA whose faces adorned the album covers, but was a key supporting musician for the group as it achieved stardom.
Brunkert played on the group's first single "People Need Love", their Eurovision hit "Waterloo", and consistently on a great many of their recordings throughout the 1970s.
As reported in The Times of 18 March 2008, he bought a property in the Betlem housing complex in Artà, Majorca, Spain, in the 1980s and lived there for the remainder of his life.