The Cubs acquired Morgan from the Guardians on Wednesday, Jeff Passan of ESPN.com reports.
The Guardians recalled Morgan from Triple-A Columbus on Sunday.
The Guardians optioned Morgan to Triple-A Columbus on Thursday.
The Guardians activated Morgan (elbow) from the 15-day injured list Saturday.
The Guardians placed Morgan on the 15-day injured list Sunday with right elbow inflammation.
The Guardians reinstated Morgan (shoulder) from the injured list Tuesday, Mandy Bell of MLB.com reports.
Morgan (shoulder) made the second appearance of his rehab assignment Tuesday with Triple-A Columbus, recording one out while giving up two earned runs on zero hits and two walks.
The Guardians placed Morgan on the 15-day injured list Wednesday with right shoulder inflammation, Joe Noga of The Cleveland Plain Dealer reports.
Morgan (1-0) allowed an unearned run on one hit and struck out two without walking a batter to earn the extra-inning win over the White Sox on Wednesday.
Morgan has allowed one run on one hit and struck out three over three Cactus League innings.