Iglesias will receive $9 million in 2020 and $9,125,000 in 2021 under the contract announced last week.
His new deal replaces a $27 million, seven-year agreement reached in 2014 that allowed him to void the remainder of the deal once he was eligible for salary arbitration. That agreement called for $5 million salaries in each of the next two seasons.
Iglesias made $4.5 million this year, when he had a career-high 30 saves in 34 chances and a 2.38 ERA.
His new deal contains bonuses for making the All-Star team, winning a Gold Glove, finishing among the top three in Cy Young Award voting, winning World Series and League Championship Series MVP and finishing among the top three for the reliever of the year award.