"Like I've been saying, I didn't want to go out like that," said Rivera, who tore his right anterior cruciate ligament in a May 3 batting practice mishap. "I didn't want that to be the last image. But it wasn't an easy decision, because there's more than just baseball with me.
"I have to consider my family and the church, too. But I feel like we have a great group of guys and a team that can compete for a championship. I'm not just coming back to play. I'm coming back to win."
The Yankees announced additional roster moves on Friday, claiming right-hander Jim Miller off waivers from the Athletics. Miller, 30, was 2-1 with a 2.59 ERA in 33 relief appearances with Oakland in 2012.
New York also signed infielder Jayson Nix to a Major League contract, avoiding arbitration. In order to make room for Rivera and Miller on the 40-man roster, the Yankees designated Nix and right-hander Mickey Storey for assignment.
Rivera, who turned 43 on Thursday, was 1-1 with a 2.16 ERA in just nine appearances for the 2012 Yankees.
The owner of 608 regular-season saves, plus a Major League-record 42 in the postseason, Rivera had recorded at least 25 saves in 15 consecutive seasons (1997-2011) and has reached the 30-save plateau 14 times in his career, tying Trevor Hoffman for the most all-time.
The Yanks expect Rivera to reclaim his role as closer after turning it over to Rafael Soriano, who converted 42 saves in 46 opportunities before opting out of his contract to declare free agency.
The $10 million figure is a step down from the two-year, $30 million pact that Rivera just completed, but the veteran will be given the opportunity to make up the difference by achieving incentives.
After briefly flirting with retirement and telling general manager Brian Cashman that he wasn't sure what he wanted to do, Rivera confirmed earlier this month that he had decided to return.
"I felt like, I have something left and [I should] give it a shot. Why not?" Rivera said.
Following his June 13 procedure, Rivera said that he has been seeing results from intense rehab with the help of a New York-based trainer. The Yankees believe that he will have plenty of time to prepare for the beginning of the '13 season.
"I have a long time to go. I'm not rushing," Rivera said. "I just have to make sure that my knee gets stronger. It does. It's getting stronger and stronger every day. I'm happy with that. I just have to continue what I'm doing."