In exchange for Smith Cleveland will be sending left-hander Tom Pannone and infielder Samad Taylor to Toronto.
According to USA Today’s Bob Nightengale neither of the two prospects are among the Indians’ top 30.
Fox Sports’ Ken Rosenthal was the first to report that Smith was on the move.
Smith, 33, is an 11-season major-league veteran. He came to the Blue Jays after signing a one-year, $3-million contract with the club in February.
He’s posted a 3.28 ERA with 51 strikeouts and 10 walks over 35.2 innings pitched mainly in a setup role for Toronto this season.