"He's the type of guy you hate to play against," Sharks GM Doug Wilson said. "You want him on your side. He doesn't care about anything other than winning."
Burish, 29, is a physical forward who played mostly on the fourth line in Dallas last season. He had six goals, 13 assists, 76 penalty minutes and a plus-6 rating.
Burish has 25 goals and 29 assists with 490 penalty minutes in 297 career games. He played his first four seasons in Chicago, winning the Stanley Cup in 2010, before spending the last two years with the Stars, where he missed the playoffs.
"I miss that suffering, that kind of pain, playing tired, playing hurt," he said. "As crazy as that sounds, I miss that. I want to figure out how to win a Stanley Cup again. San Jose, to me, should be a team competing for the Stanley Cup every year."