Trevor May of the Minnesota Twins pitches in the ninth inning...

Trevor May of the Minnesota Twins pitches in the ninth inning against the Chicago White Sox at Guaranteed Rate Field on September 16, 2020 in Chicago, Illinois.  Credit: Getty Images/Quinn Harris

Righthanded reliever Trevor May and the Mets agreed to a two-year contract on Tuesday, sources said, bolstering a bullpen that badly needs it.

The contract, worth about $15 million, was pending May passing a physical.

May, 31, joins the Mets after posting a 3.86 ERA and 1.16 WHIP with the Twins in 2020. He struck out about 40% of the batters he faced — 11th-best among qualified relievers, with Mets closer Edwin Diaz among those ahead of him — and featured the best fastball velocity of his career at 96.3 mph.

May also throws a slider about one-third of the time and mixes in a changeup, a three-pitch mix that stems from his time as a starter, before he converted to full-time relief in 2016.

Since returning from Tommy John surgery in July 2018, May has a 3.19 ERA and 1.08 WHIP. Only 10 relievers have been better in both categories in that time (minimum 100 innings).

In Queens, he will reunite with pitching coach Jeremy Hefner, with whom he worked in Minnesota during the 2019 season, the best of his career.

May will be among manager Luis Rojas’ late-inning options, the most noteworthy addition yet to a relief corps that has been an organizational weakness for years, including at the end of team president Sandy Alderson’s run as general manager.

In the Mets’ 59 seasons of existence, four of their six worst bullpen seasons have come in the past four years. They ranked 18th in the majors with a 4.60 bullpen ERA in 2020. That was an upgrade over the previous season, when their 4.99 mark was 26th.

That is the context in which the bullpen has become an early offseason area of focus for the Mets, who also need a catcher and could use rotation help and a centerfielder. In addition to May, the Mets have added righthander Jacob Barnes (claimed off waivers from the Angels), righthander Nick Tropeano (claimed off waivers from the Pirates) and righthander Sam McWilliams (who received a big-league contract despite not having pitched in the majors).

They join several relievers already under contract for 2021: Jeurys Familia, Dellin Betances and Brad Brach — all righthanders. Then there are those who are under team control but technically don’t have contracts yet: Diaz, Miguel Castro, Chasen Shreve, Robert Gsellman, Drew Smith, Paul Sewald and Daniel Zamora.

Seth Lugo has been the Mets’ best bullpen arm the past three years but finished 2020 in the rotation. His role is uncertain.

That makes for an awfully full-looking bullpen, with spring training still 2 1/2 months away.

The only lefthanders among the names above are Shreve and Zamora. If the Mets want another southpaw — say, to replace Justin Wilson, who is a free agent again after posting a 2.91 ERA in two seasons with the Mets — Brad Hand is the top option on the open market.

Hand, who turns 31 in March, is a free agent after cost-cutting Cleveland declined his $10 million option for 2021. He has a 2.70 ERA since becoming a full-time reliever in 2016.

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