The person spoke on condition of anonymity Thursday because the Mariners have not announced the deal.
The contract is expected to have a base salary for a fraction of $7.75 million the 30-year-old Bedard made last season, and it would likely include incentive clauses.
Seattle essentially would be making a low-risk move with Bedard. The Mariners no longer need him to be a top of the rotation pitcher after trading for former Cy Young Award winner Cliff Lee to team with ace Felix Hernandez, who was recently given a $78 million deal.
Bedard has said since last summer that he wanted to return to Seattle.
"I am truly happy," Bedard, in reference to the Mariners agreement, told Le Droit, a French-language newspaper in Ontario. "It was my first choice to return to Seattle. I think the team will be really good this season. I very much like the direction the team is going.''
The former Baltimore Orioles ace has been rehabilitating in his native Canada from surgery in August to repair a torn labrum in his pitching shoulder. Mariners trainer Rick Griffin has been overseeing Bedard's recovery from afar because the team is financially responsible for it until the free agent signs with another team.
Griffin said last week that Bedard felt good. He reported Bedard has been throwing and working through exercises with a physical therapist near his home in Ontario. But he added that Bedard has three-to-five months left of rehabilitation.
"He's got a ways to go," the trainer said.
The Mariners declined to offer Bedard salary arbitration this winter.
Seattle paid him $14.75 million for two seasons in which he won 11 games in 30 starts. Shoulder troubles kept him from pitching past July 4 in his first season with the team in 2008.
He had surgery in September, then was on the 2009 active roster for just 20 days past June 17 before his next surgery.
When he has pitched for the Mariners, he has rarely lasted deep into games.
The trade for him -- which cost Seattle eventual All-Stars in closer George Sherrill and outfielder Adam Jones -- has been seen as one-sided. The deal helped doom then-general manager Bill Bavasi, who was fired by the Mariners before the 2008 season ended.
For Seattle, bringing back Bedard for even half a season is a low-risk investment.
Bedard was 28-16 while averaging nearly 200 strikeouts per season for Baltimore in 2006 and '07. He was 6-4 with a 3.67 ERA with Seattle in 2008 before the shoulder woes.
If he can pitch again by the summer, Bedard would likely enter Seattle's rotation behind Hernandez, Lee and returning left-hander Ryan Rowland-Smith. The Mariners also have right-hander Ian Snell, who has a salary of about $4.4 million for 2010.