The deal is worth a reported $1.2 million with an additional $100,000 in incentives.
Aceves spent last season with the Red Sox after playing his first three seasons with the New York Yankees.
He pitched to a 10-2 record with a 2.61 ERA and two saves in 55 appearances -- four starts -- for Boston. He had career-highs of 80 strikeouts, 42 walks and 114 innings for the Red Sox.
Through his four-year career, Aceves has a 24-3 record with a 2.93 earned run average in 114 games with nine starts.
Boston's lone player left available for arbitration is designated hitter David Ortiz.