He will receive a two-year deal, a baseball source told ESPN.com on Monday. The team scheduled a press conference for 11:30 a.m. ET on Wednesday to announce the signing.
The deal would be for a total of about $15.5 million, a source said.
Cameron had to pass a physical exam for the deal to become official.
Cameron, 36, is a .250 career hitter with 265 home runs in 15 seasons with the White Sox, Cincinnati, Seattle, San Diego, the Mets and Milwaukee. He has a reputation as a positive clubhouse presence and is a three-time Gold Glove Award winner.
The Cubs, Braves and Mariners all expressed interest in Cameron, who has been a center fielder throughout his career. But the Cubs weren't willing to commit to Cameron until they were able to move outfielder Milton Bradley off their payroll, and Seattle is among the teams pursuing Bay.
Cameron has played 1,699 games in center, 139 in right and only three games in left in the big leagues, but he recently expanded his list of suitors by expressing a willingness to shift to a corner spot. Cameron's willingness to switch positions recently enticed Seattle to consider him as a possibility.
It's believed the Red Sox will make Cameron their regular left fielder, with Jacoby Ellsbury in center field and J.D. Drew in right. Jeremy Hermida, recently acquired from Florida, would serve as Boston's fourth outfielder.
Jerry Crasnick covers baseball for ESPN Insider. Information from The Associated Press contributed to this report.