The deal could pay the right-handed Petit up to $3 million based on incentives for games pitched, agent Rafael Godoy said Sunday night.
"He's excited to return. It was his first choice all along,'' Godoy told the AP via text message. "The team had been in contact all winter.''
Also Sunday, Oakland was closing in on a $2.25 million, one-year deal with veteran righty reliever Sergio Romo, sources told ESPN's Jeff Passan. Romo also still must pass a physical.
The two additions for the reigning AL West champions would provide significant experience to manager Bob Melvin's bullpen that lost closer Liam Hendriks in free agency to the Chicago White Sox. Petit and Romo have 13 years of major league experience apiece, and both pitchers are plenty familiar with the Bay Area having also played for the San Francisco Giants.
The 36-year-old Petit will return for a fourth season in Oakland, having gone 2-1 with a 1.66 ERA over 26 outings and 21⅔ innings during the shortened 60-game 2020 season. He is versatile given his ability to pitch multiple innings.
Romo, who turns 37 on March 4, was 1-2 with a 4.05 ERA and five saves and 23 strikeouts in 24 appearances and 20 innings last year for Minnesota.
A's pitchers and catchers are due to report Tuesday to the club's spring training facility in Mesa, Arizona. The first workout is Wednesday. Oakland has reached the playoffs each of the past three years -- losing the AL wild-card game in 2018 and 2019, then being eliminated in a four-game division series by the rival Houston Astros last year -- but faced scrutiny for a quiet offseason.
The Athletic was first to report Romo's pending signing.
The Associated Press contributed to this report.