The deal, which is pending a physical, was first reported Saturday by Yahoo! Sports.
Cecil's deal also includes a full no-trade clause, according to Fox Sports.
Cecil, 30, went 1-7 with a 3.93 ERA in 54 games with Toronto last season, his eighth with the Blue Jays. The left-hander missed six weeks early in the season because of a strained triceps but was a key contributor down the stretch for the Blue Jays, posting a 3.18 ERA after the All-Star break.
Cecil was a first-round draft pick of the Blue Jays in 2007, when he was selected with the 38th overall pick.