The trade was first reported by FoxSports.com on Friday.
"I never really had a say in it," Stairs said Friday. "They told me I was going to a contending team and that made it a little easier to accept than if I was going to a team that was out of the race. That would have been different.
"This is a good opportunity for me."
ESPN The Magazine's Buster Olney reported the Phillies will send the Blue Jays left-handed minor league pitcher Fabio Castro in return for Stairs. He's 8-4 with a 4.71 ERA overall this season.
Stairs is expected to join the Phillies in Chicago, where they have dropped the first two games of an important four-game set against the Cubs.
"It will be a good fit for Matt," said Blue Jays general manager J.P. Ricciardi, who was in New York Friday to see Toronto in its last trip to Yankee Stadium. "They had Geoff go down and needed someone off the bench. He should be able to help them."
Jenkins was placed on the 15-day disabled list last week with a strained right hip flexor and could be out for the rest of the regular season.
The Phillies have had discussions about several left-handed hitters in the past few days -- primarily Stairs, Minnesota's Mike Lamb and Atlanta's Mark Kotsay, who ended up being dealt to Boston.
Stairs, 40, has played the outfield and first base extensively in his career, but has started only 14 games in the field this year, all of them in the outfield. He has been the Blue Jays' primary DH since May this season, following the release of Frank Thomas.
He hit 21 home runs in only 357 at-bats last year, but has slumped this season, hitting just 11 homers and slugging only .394. But he is a .444 career hitter in Citizens Bank Park, with six home runs in only 27 at-bats.
Jayson Stark is a senior baseball writer for ESPN.com. ESPN.com senior writer Jerry Crasnick and ESPN The Magazine senior writer Buster Olney contributed to this report. Information from The Associated Press was used in this report.