Gaudin's agreement Monday was worth $2.95 million. Logan's contract was for $590,000.
The Yankees got Gaudin from San Diego on Aug. 6 for cash. The 26-year-old righty went 6-10 overall with a 4.64 ERA. He can earn another $175,000 this year in performance bonuses based on innings.
Gaudin is 34-35 lifetime with a 4.50 ERA for Tampa Bay, Toronto, Oakland, the Chicago Cubs, San Diego and the Yankees.
The 25-year-old Logan was acquired by the Yankees with pitcher Javier Vazquez from Atlanta for outfielder Melky Cabrera and pitchers Mike Dunn and Arodys Vizcaino on Dec. 22. The left-handed Logan is 5-5 lifetime in the majors with a 5.78 ERA.