The news was first reported by Mike Francesa of WFAN, who added that the announcement will come early next week.
The physical is expected to be extensive. It is believed the deal will be for about $66 million over four years plus a vesting option for a fifth year. Bay was looking for a six-year deal originally, and most recently a five-year, $80 million offer.
Bay batted .267/.384/.537 for the Red Sox in 2009 with 36 home runs and 119 RBIs. He came to Boston in July 2008 in the three-way trade with the Dodgers and Pirates that sent Manny Ramirez to Los Angeles. Bay helped the Red Sox reach the postseason each of the past two years, but he had just one hit and no RBIs in Boston's three-game sweep at the hands of the Angels in the 2009 American League Division Series.
Bay won the 2004 National League Rookie of the Year award with the Pirates and is a three-time All-Star.
The Mets are still hoping to add a starting catcher and one or two starting pitchers this offseason. They have been in discussion with free-agent catcher Bengie Molina, who is their first choice at the position, but they haven't yet acceded to his request for a three-year $20-million deal. The Mets' first pitching choice among free agents is Joel Pineiro, but they also have interest in Doug Davis and Jon Garland.