SAN FRANCISCO >> Two-time NL Cy Young Award winner Tim Lincecum has finalized his $35 million, two-year contract with the San Francisco Giants after passing a physical Friday.

Just as the Giants had hoped, they signed Lincecum before he went on the free-agent market.

Lincecum reached agreement on the new deal earlier in the week that keeps him with his only major league team through 2015. The contract pays $17 million for next year and $18 million in 2015.

Lincecum’s contract includes a full no-trade clause. In addition, he can earn an additional $250,000 each for 210 innings pitched and 220 innings.

He just completed a $40.5 million, two-year contract that paid him $22 million this season.

Given the uncertainty in the rotation, keeping one of the club’s most notable faces means a lot to manager Bruce Bochy.

“He is an important part of our rotation and we are very pleased to have him back for at least two more years,” assistant general manager Bobby Evans said of Lincecum, who pitched a no-hitter July 13 at San Diego.

The Giants, who won the World Series in 2010 and again last year, will not exercise left-hander Barry Zito’s $18 million 2014 option, while Ryan Vogelsong might not return.

Lincecum said late in the season he is a creature of familiarity and hoped to stay put with San Francisco, which drafted him 10th overall out of Washington in 2006 and quickly promoted him to the majors in May 2007.

He pitched the Game 5 World Series clincher at Texas in 2010, when the Giants captured their first championship since moving West in 1958. Then in 2012, Lincecum moved to the bullpen for the playoffs and emerged as a reliable reliever as San Francisco won another title.

Lincecum — the Cy Young winner in 2008 and ’09, when he won 18 and 15 games, respectively — went 10-14 with a 4.37 ERA and 193 strikeouts over 32 starts last year, his third straight season with a losing record. The right-hander joined Hall of Famers Juan Marichal and Gaylord Perry and also Kirk Rueter as the only Giants in San Francisco history to win at least 10 games in six straight seasons.

The 5-foot-11, 170-pound Lincecum earned the nicknames The Freak and Franchise for his quick rise to the majors and his quirky delivery. A four-time All-Star, he is 89-70 with a 3.46 ERA over seven major league seasons.

There was some thought he might test the open market and at least listen to any offers from his hometown Seattle Mariners.

General manager Brian Sabean has now checked off two important items from his to-do list looking forward to what he hopes is a comeback year for the club in 2014. In late September, the Giants signed right fielder Hunter Pence to a $90 million, five-year contract before the season ended. He played every game this year.

Zito, who recently took out a full-page newspaper ad thanking Giants fans, will be due a $7 million buyout as he departs following a $126 million, seven-year contract. The move will be made formal at the conclusion of the World Series.