A person with knowledge of the situation confirmed the deal to The Associated Press on Thursday on the condition of anonymity because no formal announcement has been made.
The 34-year-old Burrell came to the Giants on a minor league deal May 29 after his release by Tampa Bay and spent a short stint with Triple-A Fresno before joining the Giants on June 4.
He batted .266 with 18 home runs and 51 RBIs in 96 games for San Francisco, becoming the everyday left fielder. Burrell was a key member of a team dubbed "characters and misfits" by manager Bruce Bochy. The Giants clinched the NL West on the season's final day, ending a six-year playoff drought.
Burrell, who also won a ring with the Phillies in 2008, struggled in the World Series -- won in five games by the Giants over the Texas Rangers. He went 0 for 13 with 11 strikeouts and was benched for Game 4 at Texas. He had 22 strikeouts in 49 at-bats overall during the postseason.
General manager Brian Sabean has said he didn't know whether the Giants would be able to re-sign Burrell, though first baseman Aubrey Huff certainly hoped so after receiving a new $22 million, two-year contract last week.
After losing infielder Juan Uribe to the rival Los Angeles Dodgers earlier this week, San Francisco also agreed on a $6.5 million, one-year contract with free-agent shortstop Miguel Tejada on Tuesday.
Sabean's priorities had been to fill the other spots first, so the move with Burrell happened sooner than expected.
Sabean and Bochy have praised Burrell for his leadership in the clubhouse and on the field.