The 33-year-old Cotts had been eligible for salary arbitration before Wednesday's agreement.
Cotts was 8-3 with a 1.11 ERA in 58 games last season. He struck out 65 in 57 innings.
Cotts began the season at Triple-A before being promoted on May 21 for his first big league action since 2009. He was out in 2010 and 2011 because of injuries.
He is 18-15 with a 3.99 ERA in 342 games with the Chicago White Sox, Cubs and Rangers.
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