The deal is a record-high salary for a player in an arbitration year. Price was one of 175 players who filed for arbitration earlier in the week.
The 29-year-old was traded from the Tampa Bay Rays to the Tigers at July's trade deadline. He had previously spent his entire career with the Rays, winning the Cy Young Award in 2012.
In 2014, Price went 15-12 with a 3.26 ERA and a league-leading 271 strikeouts in 248.1 innings, including a 4-4 mark with a 3.59 ERA in 11 starts for Detroit.
A four-time All-Star, Price earned $14 million last season.
- Molly Geary