Growing up in Eskilstuna it was only natural for him to play for the towns handball team, GUIF, and he was moved up to their senior squad, making his debut in the Swedish top division at the age of 15.

In 1988, at the age of 20, he made his first cap for Sweden and in 1990 he was one of the main forces in the national team who won the World Championship in Czechoslovakia.

This success landed him a contract with Atlético Madrid BM in Spain where he played for some time before moving to CD Bidasoa.

Right after this he moved to Barcelona where he stayed for several seasons, helping the team become the most prominent handball team in the world, winning just about everything there is to win – including international competitions like EHF Champions League and EHF Men's Champions Trophy as well as Spanish competitions like Liga ASOBAL and Copa del Rey de Balonmano.

Svensson moved to Germany and HSV Hamburg for a short while before returning to Spain, this time to play for Portland San Antonio.