The 34-year-old righty, who last pitched on Feb. 6 in the Caribbean World Series, is expected to arrive in camp Tuesday.
The agreement was first reported by ESPN.com's Jerry Crasnick.
If he makes the Opening Day roster, Colon would provide rotation insurance for Boston, which will be without Curt Schilling, who is working his way back from a shoulder injury.
The team's medical staff will evaluate the two-time All-Star, who has gone 7-13 with a 5.72 ERA while slowed by shoulder and elbow injuries the past two seasons. Colon suffered through an injury-marred 2007 for the Los Angeles Angels, posting a 6-8 record and a 6.34 ERA -- the worst of his career. If he is added to the Red Sox 40-man roster, he would get a $1.2 million, one-year contract and have the chance to earn performance and roster bonuses.
"He's going to show up here in camp and we'll do an evaluation of how far he is away from helping us," general manager Theo Epstein told The Associated Press. "It takes more than five starting pitchers to get through a season. Obviously, he's an accomplished guy and if we can get him back to a point where he's throwing well, he can certainly help us."
Epstein told the AP that Red Sox scouts came back with "decent" reports from Colon's performance in the Caribbean Series, where the burly right-hander's fastball reached the low 90s mph after elbow inflammation kept him off the Angels' playoff roster in the fall.
Those evaluations, coupled with a conference call between Colon, Epstein and manager Terry Francona last week, convinced the parties to move forward.
"I think he had some things to sort out," Francona said. "We just wanted to sell the Boston situation, at the same time being very honest and making sure he knew he was welcome."
The White Sox, Cardinals and Astros also had been rumored as possible suitors for Colon this offseason. According to Olney, Colon was close to an agreement with the
Mets earlier this winter, but New York backed off out of concern for the condition of his pitching arm.
In his 11-year career, Colon is 146-95 with a 4.10 ERA. He is a two-time 20-game winner, and he won the Cy Young Award in 2005 with the Angels. He is expected to start a throwing program immediately.
"He knows he's a big league pitcher. He knows he can pitch effectively at the highest level when he's healthy, and he wanted to do so in a competitive environment," Epstein said. "We'll just get him here and outline a program to get him back into top pitching shape and see what comes of it."
Francona, who first saw a 23-year-old Colon when he was "throwing 1,000 [mph]" in the Dominican Republic in 1996, said he was also cautiously optimistic about the two-time 20-game winner.
"Best case?" Francona said. "Who knows, but this kid's got a good history behind him as a major league pitcher."
Information from ESPN.com's Jerry Crasnick and The Associated Press was used in this report.