The team also announced before Tuesday night's game at Tampa Bay that infielder Brett Lawrie was transferred from the 15- to the 60-day disabled list, which ends his regular season.
Lawrie went on the DL in early August with an oblique injury.
''Continue his rehab and get ready for spring training,'' Toronto manager John Gibbons said. ''There was not enough time.''
Morrow had been sidelined because of an injured right finger since early May, and he'll work out of the bullpen. Johnson missed a month with a strained left hamstring.
Second baseman Ryan Goins, outfielder Anthony Gose, right-hander Kendall Graveman and left-handers Sean Nolin and Daniel Norris were recalled from Triple-A Buffalo.
Outfielders Dalton Pompey and catcher George Kottaras had their contracts purchased from Buffalo.
Outfielder Darin Mastroianni and first baseman Matt Hague were designated for assignment. Right-hander Neil Wagner was released.