Hughes' new deal is worth $2.7 million, while Chamberlain will earn $1.4 million. Logan has agreed to a $1.2 million contract.
Hughes, 24, was an All-Star for the first time in 2010, going 18-8 with a 4.19 ERA in 31 games (29 starts), setting career highs in wins, losses, innings pitched (176 1/3) and strikeouts (146).
The youngest Yankees right-hander to win at least 18 games in a season since 23-year-old Mel Stottlemyre won 20 games in 1965, Hughes earned $447,000 as he pitched in his fourth Major League season.
Chamberlain, 25, was 3-4 with three saves and a 4.40 ERA in a team-leading 73 appearances for the Yankees last year, working exclusively out of the bullpen for the first time in his professional career.
Projecting to continue in a relief role as the Yankees prepare to head to Spring Training and with a return to the rotation having been ruled out by club, Chamberlain earned $487,975 for his services in 2010.
Logan, 26, was 2-0 with a 2.93 ERA in 51 relief appearances for the Yankees in 2010, serving for most of the season as their lone left-hander in the bullpen.
Acquired before the season in a trade with the Braves, Logan earned $590,000 from the Yankees after agreeing to a contract offer, avoiding arbitration in his first year of eligibility.
He figures to enter 2011 complementing Pedro Feliciano as the left-handers in New York's bullpen.
The Yankees have not gone to arbitration since February 2008, when they prevailed in their case against right-hander Chien-Ming Wang.
The Yankees avoided arbitration earlier this winter with right-hander Sergio Mitre, who signed a contract worth approximately $900,000 on Dec. 1. Mitre figures to compete for a starting role in the back of New York's rotation.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.