Late Wednesday, right-hander Sergio Mitre agreed to a one-year contract with the club worth approximately $900,000.
New York also offered 2011 deals to pitchers Joba Chamberlain, Phil Hughes and Boone Logan. If a player had not been tendered a contract by 11:59 p.m. ET, he immediately would become a free agent and be able to negotiate with any team.
Moseley, 28, attended camp on a Minor League deal and was promoted to the big leagues in July, slotting into the rotation when the Yankees needed to patch over the absence of the injured Andy Pettitte.
Finishing 4-4 with a 4.96 ERA in 16 games (nine starts), Moseley recorded all of his decisions in starting efforts. As a reliever, Moseley had a 3.77 ERA over 14 1/3 innings.
Moseley also pitched two scoreless innings of relief in Game 1 of the American League Championship Series, earning his first postseason victory when the Yankees stunned the Rangers with a five-run eighth inning to post a 6-5 win.
Aceves, 28, struggled through a season that was cut short to injury. Plagued by back issues, Aceves was unable to get back on the mound for the Yankees after beginning the year 3-0 with a 3.00 ERA in 10 relief appearances.
Aceves suffered another setback this month, as he required left clavicle surgery following a bicycle accident in Mexico. The surgery was performed Tuesday in New York, and Aceves is expected to need three months for full recovery.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.