The contract is worth $8 million, according to ESPN and multiple reports.
The 38-year-old lefty has played the past 10 seasons of his 18-season career with the Yankees. In his announcement on Twitter, Sabathia said of the deal for the 2019 season: "This'll be it."
Sabathia went 9-7 with a 3.65 ERA in 29 starts last year for a 100-win New York club that lost in the American League Division Series to the Boston Red Sox.
He took a cut in salary from $25 million in 2017 to $10 million in '18. An ejection in his final start of the regular season cost Sabathia a $500,000 bonus that he would have earned for reaching 155 innings pitched.
Sabathia, who underwent right knee surgery in October, is one of just three returning members of the Yankees' 2018 rotation, joining Luis Severino and Masahiro Tanaka. Starter J.A. Happ is a free agent, and Yankees general manager Brian Cashman had said the team hopes to re-sign him, as well.
New York already this offseason re-signed Brett Gardner, so keeping Sabathia maintains two veteran presences in the clubhouse.
"These are known commodities," Cashman said. "We know exactly who they are in that clubhouse, who they are dealing with our press and our fans, and obviously -- most importantly -- competing on the field of play."