The 29-year-old righty had been eligible for salary arbitration before Wednesday's deal. He made $7.35 million last season.
Allen was 3-7 with 30 saves and a 2.94 ERA for the American League Central champions. Cleveland led the AL with 102 wins before losing to the Yankees in the division series.
Allen has posted at least 30 saves in each of the past three years. The Indians have benefited from a deep bullpen that included Andrew Miller, but have lost relievers Bryan Shaw and Joe Smith to free agency since the season ended.