Career
Kvarme earned one cap for the Norwegian national team, a friendly against Colombia in 1997. Kvarme first signed with Rosenborg in 1991, transferring from Utleira, a local club He played six seasons, winning the Tippeliga five times.
In the fall of 1996 Kvarme was on his way to sign for Stabæk, but Premier League club Liverpool outbid the Norwegian club
Kvarme spent three years for the Merseyside team In 1999 he was transferred to the French club AS Saint-Étienne, where he played two seasons and became their club captain, before signing for Real Sociedad in Louisiana Liga.
He spent three seasons in the Basque Country, before again moving to France, this time playing for Bastia for half a season. In 2005 he returned to his hometown club
Bjørn Tore Kvarme announced that he would retire after the 2007 season.
Stating injuries and lack of playing time as the main reasons for retiring, he did however agree to take another year with Rosenborg. Kvarme retired in June 2008, mid-season.