Allen had agreed to the deal that is worth $8.5 million, according to multiple reports, after a disappointing 2018 that saw his ERA balloon to 4.70 following five consecutive seasons of sub-3.00 ERA pitching.
The 30-year-old Allen had been a longtime workhorse for the Indians, who rode him heavily during their 2016 run to the World Series. The deal is pending a physical.
The Angels are banking on a return to form and hope Allen can mentor their hard-throwing bullpen that includes Justin Anderson, Ty Buttrey, Hansel Robles, Noe Ramirez, Cam Bedrosian and Luis Garcia, whom they acquired from Philadelphia over the winter. Also returning should be erstwhile closer Keynan Middleton, who underwent Tommy John surgery in May 2018.
Allen, who has played his entire major league career for the Indians, is coming off a subpar season in which he registered career worsts in ERA (4.70 ERA) and save percentage (84.4).
He struck out 80 batters in 67 innings, but his walk rate increased from 2.8 percent in 2017 to 4.4 percent in 2018, he had a higher home run rate (1.5 percent), and he especially struggled down the stretch.
A durable and consistently effective closer in previous seasons, Allen was 3-7 with 30 saves and a 2.94 ERA for the AL Central champions in 2017 when Cleveland led the American League with 102 wins before losing to the Yankees in the division series. The righty ranked sixth in the AL in saves and had 30 or more for the third consecutive season.
Allen was also an integral component of a Cleveland bullpen two years ago that led the way when the Indians overcame significant injuries in their starting rotation and won the AL pennant. He recorded 32 saves in 35 tries and further established himself as a top-flight finisher.
Allen's 149 total saves, including a career high of 34 for Cleveland in 2015, are the ninth-most among active players and the most in Indians history.
The Angels designated right-hander Miguel Almonte for assignment in a corresponding move.