Johnson, who joined Toronto in the off-season as part of a blockbuster trade with the Miami Marlins, is scheduled to start for the Blue Jays on Tuesday night against the Giants in San Francisco.
The 29-year-old has missed the last six weeks with a right triceps injury. In four starts for Toronto in 2013, Johnson is 0-1 with a 6.86 earned-run average.
Davis, meanwhile, returns after recovering from a left oblique strain.
The 32-year-old hasn't played since May 10. In 26 games this season, he has a .284 average with one home run, four RBIs and eight stolen bases.
The team also placed right-hander Ramon Ortiz on the 15-day DL on Tuesday.
The 40-year-old left the game in tears on Sunday in San Diego after suffering a right elbow strain in the third inning. He was scheduled to undergo an MRI exam later Tuesday.
Ortiz has made four starts and seven appearances for the Blue Jays this season. He has a 1-2 record with a 6.04 ERA.