Financial terms were not disclosed by the club, but CBSSports.com reported that Chamberlain, 26, will earn approximately $1.675 million, while Robertson, 26, will receive $1.6 million plus $25,000 in incentives.
Three Yankees remain eligible for arbitration. Catcher Russell Martin filed for $8.2 million, while the Yanks offered $7 million; outfielder Brett Gardner filed for $3.2 million and the club offered $2.4 million; and left-hander Boone Logan asked for $2.1 million and was met with a $1.7 million offer.
New York's bullpen was one of its biggest strengths in 2011, due in no small part to Robertson's emergence as an American League All-Star and one of the game's top setup men.
Robertson was 4-0 with one save and a 1.08 ERA in a team-leading 70 appearances, pacing all AL relievers in ERA and placing second in the Majors only to the Braves' Eric O'Flaherty (0.98).
Nicknamed "Houdini" for his uncanny ability to escape tight jams, Robertson limited opponents to a .170 (40-for-235) batting average and prevented 34 of 44 (77.3 percent) inherited runners from scoring.
Over his four Major League seasons, all with the Yankees, Robertson owns a 14-6 record with a 3.03 ERA in 204 games. He receives a sizable boost in salary after earning $460,450 in 2011.
Chamberlain was 2-0 with a 2.83 ERA in 27 appearances last season before undergoing season-ending Tommy John surgery on June 16. He earned $1.4 million in 2011.
Chamberlain has said that he hopes to break camp with the Yanks in April, but the club is eyeing a more conservative timeline and expects to have the right-hander back by June or July.
In five Major League seasons, all with New York, Chamberlain is 20-13 with a 3.70 ERA in 193 games (43 starts).
Right-hander Phil Hughes agreed to a deal on Monday worth $3.2 million plus performance bonuses, avoiding arbitration. Tuesday marked the deadline for teams and eligible players to submit arbitration figures.
Martin earned $5,375,000 last season, his first year with New York. Gardner made $529,500 and Logan earned $1.2 million. Players and teams who go to arbitration hearings will engage in that process from Feb. 1-21 in St. Petersburg.