The deal, which is pending a physical, was first reported by MLB Network. Suarez can opt out after three years and become a free agent again, the reports said.
Suarez, a 31-year-old rookie, was having a terrific postseason until allowing Bryce Harper's go-ahead, two-run homer with no outs in the eighth inning of Game 5 of the National League Championship Series that sent the Philadelphia Phillies to the World Series.
Manager Bob Melvin was criticized by some for letting Suarez pitch to Harper instead of using left-hander Josh Hader. Melvin said Hader wasn't ready when Harper came to bat and that he wanted to get through the final three innings with Suarez and Hader, the Padres' two best relievers. Melvin said he wanted to get two outs from Suarez in the eighth and the final four outs from Hader. Philadelphia won 4-3.
Suarez, who is represented by Amuse Sports, will make salaries of $10 million in each of the first three years of the deal and $8 million in the last two. Additionally, he can make up to $3 million per season if he finishes a certain number of games. Those incentives will pay off if Hader is not retained after his contract expires following next season and Suarez becomes the closer.
Suarez was especially impressive in the NL Division Series win over the Los Angeles Dodgers, throwing four scoreless innings in three appearances. He pitched two scoreless innings in a wild-card series win against the New York Mets.
He went 5-1 with a 2.27 ERA in 45 appearances during the regular season.
The Associated Press contributed to this report.