The deal was worth $1.4 million in the 2011-12 season and $1.25 million in 2012-13, a source told ESPN.com.
The restricted free agent had 20 points, with four goals and 16 assists, in 68 games last season to go with 14 penalty minutes.
The 6-foot-2, 196-pound Gunnarsson was Toronto's sixth choice (189th overall) in the 2007 draft. He has seven goals and 28 assists in 111 career games with the Leafs.
Gunnarsson won a silver medal with Sweden at this year's world championships.
Information from ESPN.com's Pierre LeBrun and The Associated Press was used in this report.