Navarro, a switch hitter, is expected to back up Blue Jays regular catcher Russell Martin. Navarro played in Toronto during the 2014 and 2015 seasons.
The 32-year-old veteran signed a one-year, $4 million contract with the White Sox after last season. He is hitting just .210 with six home runs and 32 RBIs in 85 games this season.
The Blue Jays are hoping Navarro's return to Toronto will re-energize him for the final month of the regular season and possibly into the playoffs.
"I could see the smile through the phone," Blue Jays general manager Ross Atkins said. "This should be a boost of energy for him, coming into a contender."
Navarro likely will not join the Blue Jays until Monday when they begin a series in Baltimore against the Orioles.
As Navarro departs, the White Sox are ready to activate catcher Alex Avila off the disabled list.
Turner pitched in Class A and Double-A for the White Sox organization this season, posting a 3-1 record with a 1.33 ERA in 44 games.