Pierre LeBrun of ESPN.com and TSN reported the deal is worth $6.4 million, so it carries a salary cap hit of $1.6 million through the 2016-17 campaign.
Thompson, slated to be an unrestricted free agent after this season, has six goals and 10 points in 30 games for the Lightning this season. He has been a fixture on one of the bottom two lines for the Lightning in recent seasons since being claimed on waivers from the New York Islanders in 2010.
"We're very pleased to have agreed to a contract extension with Nate," Tampa Bay general manager Steve Yzerman said in a statement. "He has and will continue to be a very important member of our team both on and off the ice."