The deal, first reported by Sirius XM, could reach $6 million with incentives and is pending a physical.
Rodney went 5-4 with a 4.23 ERA and converted 39 of 45 save chances last season in his one season in Arizona. He was signed to a one-year deal in the offseason and enjoyed a reliable year as closer, as the Diamondbacks reached the National League Division Series.
After two down seasons with four different teams, Rodney bounced back with a solid campaign in 2017 and finished the season with the third-most saves in the National League. He improved his strikeout-to-walk ratio (2.50) by almost 1.
Rodney, who will turn 41 on March 18, ranks sixth in the majors among active pitchers in career saves (300) and has a 3.73 ERA in 14 major league seasons with eight teams. He made an All-Star team three times, including in 2012, when he had a career-high 48 saves and a 0.60 ERA with the Rays.
Rodney, from the Dominican Republic, is known for his shoot-the-arrow pantomime after he finishes off saves.
The Associated Press contributed to this report.