The agreement will become official once Bay passes a physical exam sometime next week, the source said. The deal includes a vesting option year that could increase Bay's overall payout to slightly more than $80 million over five years.
WFAN was the first to report the agreement had been reached.
Bay, a three-time All-Star, hit .267 with 36 home runs and 119 RBIs for the Boston Red Sox in 2009.
Bay and outfielder Matt Holliday were the most hotly pursued position players on the free-agent market this winter.
It's believed that Bay's vesting option provision includes readily attainable targets based on plate appearances. Bay has averaged 154 games a season since 2005 with Pittsburgh and the Red Sox, so he should have a good chance of making the option vest if he stays healthy.
Mets general manager Omar Minaya, chief operating officer Jeff Wilpon and several other principals in the deal are traveling or in the middle of holiday plans, so Bay's physical exam isn't expected to take place until early next week.
The Mets expect Bay to add thump to an offense that ranked last in the major leagues with 95 home runs in 2009. New York's lineup was decimated by injuries to center fielder Carlos Beltran, shortstop Jose Reyes and first baseman Carlos Delgado, and manager Jerry Manuel's team ranked 25th in the big leagues with 671 runs scored.
Bay has been maligned in some quarters for his subpar defense, but the Mets analyzed the metrics and found that he suffered in Boston from the "Fenway Park factor.'' They think his perceived lack of range in left field was accentuated by the minimal area of ground he had to cover in Fenway.
The Mets also expect that Bay's ability to pull the ball will help him in pitcher-friendly Citi Field, which is spacious in the gaps but plays fairer to hitters down the lines.
At the beginning of the free-agent process, many observers believed that Bay was destined to return to Boston. But after the Red Sox spent $82.5 million on free-agent starter John Lackey and $15.5 million on outfielder Mike Cameron, it became clear that Bay's tenure in Boston had reached an end.
"It's definitely going to be tough for all of us," Red Sox infielder Kevin Youkilis said, according to the Boston Globe. "Jason was a close friend. A joy to play with him. Great ballplayer.
"But it's a business, things happen. It's one of those business moves on each side. It just didn't work out right. I wish him the best in New York. Hopefully we get to see him in the World Series."
Bay underwent shoulder surgery in 2003 and arthroscopic knee surgery in 2006, and the Red Sox reportedly had enough concerns about his long-term health to hold firm at a four-year contract offer rather than the five-year deal that Bay was seeking.
Bay's agent, Joe Urbon, recently spoke to the Red Sox about a possible reunion. But with Cameron, Jacoby Ellsbury and J.D. Drew in the outfield mix, a Red Sox official said it was a "long shot" for Bay to return to Boston.
Bay, 31, broke into professional ball as a 22nd-round draft pick with the Montreal Expos in 2000. The Mets acquired him in a trade in March 2002, but sent him to San Diego four months later as part of a five-player deal with the Padres.
In his next stop, with the Pittsburgh Pirates, Bay made two All-Star teams and posted back-to-back, 30-homer, 100-RBI seasons in 2005 and 2006.
The Mets have had a relatively slow winter, but the Bay signing gives the team the impact bat Minaya had been seeking. New York is now expected to turn its attention to adding a catcher -- with Bengie Molina a prime target -- and acquiring an innings-eating starter for the back end of the rotation. Free agents Jon Garland and Doug Davis are among the possibilities.
Bay's .676 slugging percentage with runners in scoring position last year ranked second in baseball behind Albert Pujols' .697. Since 2005, Bay is tied for fourth among big league outfielders with 155 home runs, and ranks fifth with 514 RBIs.
Bay, a native of Trail, British Columbia, is the first native Canadian to play for the Mets since shortstop Brian Ostrosser, an Ontario product, went hitless in five at-bats in 1973.
Jerry Crasnick covers baseball for ESPN.com