The deal is worth $10 million plus incentives, sources told ESPN.
Rivera, who turned 43 on Thursday, will take a pay cut from the $15 million he earned in 2012.
The Yankees had been hoping to wrap up a deal with Rivera before the winter meetings, which start Monday in Nashville, Tenn.
Rivera was limited to nine games this year after tearing the anterior cruciate ligament in his right knee while tracking down a fly ball during batting practice in Kansas City on May 3. He is baseball's career leader with 608 saves.
Information from ESPNNewYork.com's Andrew Marchand and The Associated Press was used in this report.