NEW YORK -- In the first significant free-agent splash of the Steve Cohen era, the Mets on Wednesday signed free-agent reliever Trevor May to a two-year deal.

MLB Network insider Jon Heyman reported that the two-year contract is worth around $15 million.

The right-handed May will give the Mets an additional measure of depth at the back of their bullpen, fulfilling a stated goal of new president of baseball operations Sandy Alderson.

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May, 31, has posted a 3.19 ERA over the past three seasons with the Twins since returning from Tommy John surgery. He produced a 3.86 mark this year, while his strikeout rate of 14.66 per nine innings ranked seventh in the Majors. May’s 43-percent whiff rate was eighth. His average fastball velocity, which sat at 93.9 mph before surgery, rose for the third straight season to a career high of 96.4 mph, as May scrapped his curveball in favor of additional sliders and four-seam fastballs up in the zone.

“I think I learned a lot about what it takes to go and establish yourself at the Major League level,” May said Monday during an appearance on MLB Network Radio. “That’s invaluable to me. That’s going to be invaluable as I move forward.”

In New York, May will enter a bullpen mix that includes Edwin Díaz, Jeurys Familia, Dellin Betances, Miguel Castro and Brad Brach, along with potentially Seth Lugo if the Mets don’t use him as a starter. Alderson, who is handling baseball operations decisions while the Mets search for a general manager, has cited the bullpen as an area of concern after the Mets ranked in a tie for 18th in relief ERA (4.60) this season.

“We have a number of holes to fill,” Alderson said last week. “We talked about starting pitching, outfield, catching; we’d like to enhance the bullpen somewhat. We have a lot of places where we might invest, and it gives us some flexibility.”