The Mets also announced one-year deals with outfielder Guillermo Heredia ($1 million), who provides depth in center, and right-handed reliever Jacob Barnes ($750,000 plus $25,000 for one day on the active major league roster and $25,000 each for 25, 40 and 50 games pitched).
Shreve, a 30-year-old left-hander, was 1-0 with a 3.96 ERA over 17 appearances in his only season with the Mets, striking out 34 and walking 12 in 25 innings while allowing 17 hits. He earned $556,556 in prorated pay from his $1.5 million salary.
Shreve is a veteran of seven major league seasons with Atlanta (2014), the New York Yankees (2015-18), St. Louis (2018-19) and the Mets, going 17-8 with a 3.74 ERA in 235 relief appearances. He was traded by the Yankees with right-hander Giovanny Gallegos to the Cardinals for first baseman Luke Voit in July 2018, then became a free agent after the 2019 season.
Matz, a 29-year-old left-hander, had the poorest of his six seasons, going 0-5 with a 9.68 ERA while earning $1,851,852 in prorated pay from a $5 million salary. He was dropped from the rotation after starting 0-4 with a 9.00 ERA in five starts, then made three relief appearances along with a spot start. He is 31-41 with a 4.35 ERA over 107 career starts and five relief appearances.
May, a 31-year-old right-hander, gets $7.75 million in each of the next two seasons. He would earn $50,000 bonuses for 60, 65 and 70 games pitched, and $50,000 apiece for 60 and 70 innings.
He had a 3.86 ERA in 24 relief appearances for the Minnesota Twins last season, striking out 38 and walking seven in 23 1/3 innings while allowing 20 hits with a career-high fastball velocity averaging 96.66 mph. He earned $816,667 in prorated pay from a salary of $2,205,000.
May had spent all six big league seasons with the Twins, going 23-21 with a 4.44 ERA in 26 starts and 189 relief appearances.
He made 16 starts in 2015, going 8-9 with a 4.00 ERA over 48 appearances. May had Tommy John surgery on March 22, 2017, and returned to the major leagues on July 31, 2018.
Mets relievers tied for 18th in the majors with a 4.60 ERA last season and the team had seven blown saves in 18 chances.
New York's front office is being run by Sandy Alderson, who returned to the Mets as team president last month on the day Steve Cohen completed his $2.42 billion purchase from the Wilpon and Katz families.