Thornton had been with the Sharks since 2000, scoring 147 points and recording 439 penalty minutes in 342 games. He skated for Toronto, Edmonton, Montreal and Dallas earlier in his career, playing 836 games over parts of 15 NHL seasons.
Thornton, who scored 21 points last season, is also the cousin of Joe Thornton, the Sharks' star center and last season's NHL scoring champion.
But the 35-year-old Scott Thornton was the Sharks' oldest player last season by nearly five years. His option for next season was worth more than $1.5 million.
San Jose general manager Doug Wilson declined the chance to exercise Thornton's option and then trade him to another team, saying he wanted Thornton to be able to choose his next club.
"It's not every player you do this for, but I have a lot of respect for him," Wilson said. "This gives him time to check out his options. ... We've got guys coming from underneath, and we will look externally, too, to improve our team."
Thornton and center Alyn McCauley are the Sharks' only unrestricted free agents. The Sharks will open negotiations next week with McCauley, who was slowed for most of the playoffs by a knee injury.