The first instrument Anders played was the piano, but at the age of 14, after a bicycle accident, he switched to drums. From 1979 through 1982 he attended an electronics engineering school.
In 1984 he moved to the United States to join his brother Jens in Yngwie Malmsteen's band. He recorded 5 albums and made 5 world tours with Yngwie. After that, he worked with a huge number of artists, including bassist Jonas Hellborg, Benny Jansson, and with his brother Jens (as "The Johansson Brothers"). He initially joined HammerFall on the "Legacy" tour in 1999, at first only as a session drummer but later as a full-time member.
He is co-founder of Heptagon Records with his brother, created to promote their discs, their father's and some other Swedish musicians' work.
Anders was a guest drummer on Narnia's album The Great Fall. Anders is best known for his time in Yngwie's band, besides his former role as HammerFall's drummer. He has been praised for his technical talent, in metal as well as other genres.
Anders also plays the upright bass (double bass) in a jazz duo together with his brother Jens Johansson.