NEW YORK – A mutual need brought Marcus Stroman and the Yankees together, with optimism replacing any lingering hard feelings.

“I get the chills thinking about my first start at Yankee Stadium,’’ Stroman said Thursday, a day after his two-year, $37 million free agent contract with a vesting option for 2026 was made official.

Maybe this marriage never happens if the Yankees had signed their top rotation target, Yoshinobu Yamamoto, or pulled off a Dylan Cease trade, or somehow convinced Blake Snell – coming off a Cy Young Award season – to take half of what they offered Yamamoto, yet to throw a big-league pitch.

“I think our team overall is going to be a constant evolution,’’ said Yankees GM Brian Cashman, still open to pitching upgrades in 2024, all the way to the Aug. 1 trade deadline.

That speaks to other questions in the Yanks’ rotation, with Nestor Cortes and Carlos Rodon coming off injury-marred seasons and Clarke Schmidt being relied upon more than ever.

HOT STOVE UPDATES: MLB free agency: Ranking and tracking the top players available.

In the grand scheme, how the Yanks and Stroman got together is less important than how the right-hander might accomplish more than just stabilizing a staff.

“I think we’re capable of definitely having a deep October run,’’ said Stroman. “That’s obviously the goal.’’

Yankees, Marcus Stroman clear the air

Once the Yanks pivoted toward Stroman, with appeal for his high groundball rates and fearless mound demeanor, a few things happened.

Stroman’s social media was suddenly cleared of past posts trolling the Yankees, and Cashman cleared the air in a phone conversation with Stroman.

This trouble dated to September 2019, when Cashman told Yahoo Sports that “we were interested in Stroman but we didn’t think he would be a difference-maker.’’

Traded to the Mets from the Toronto Blue Jays that summer, Stroman followed with a critical Twitter post, comparing his superior pitching stats against the Yankees’ starters.

“It was my bad,’’ Cashman said Thursday, adding that his quote was about Toronto’s asking price.

“For the amount of talent they wanted back, (Stroman) wasn’t going to be enough of a difference-maker,’’ Cashman said. “If I didn’t value the player, I wouldn’t be trying to trade for him.’’

At the time, Cashman apologized to Stroman through Stroman’s then-agent.

Late last month, when the Yankees made their interest known to Stroman’s agent and ex-Mets GM Brodie Van Wagenen, Cashman insisted on phoning Stroman to apologize again.

“I wanted him to hear exactly what transpired and what was intended and not intended,” Cashman said. ‘He didn’t deserve how this was playing out.’’

Ready to thrive at Yankee Stadium

Stroman wasn’t seeking an explanation from Cashman.

“We kind of laughed about it and we moved on,’’ Stroman said of their recent phone conversation. “He let me know how interested he was in me as a pitcher, thought that I was someone that would thrive in the lights and the pressure.

“And I thought it was a perfect fit.’’

Growing up on Long Island as a Yankees fan, Stroman has long felt he’s built for the Bronx.

“I think a lot of guys avoid coming to New York and playing for the Yankees because of that reason,’’ Stroman said of the pressurized atmosphere. “I’m someone who feels it brings out the best in me.’’

Stroman’s fiery nature has also extended to battles on social media. “I’d say I’m misunderstood, for sure,’’ said Stroman, responding to that direct question.

But he’s eager for Yankees fans to watch him compete, “something I do at the highest level,’’ and to tap into Gerrit Cole’s knowledge while blending into the staff.

“I feel like I’m someone who adapts very easily,’’ said Stroman, adding that Cole, captain Aaron Judge, Anthony Rizzo and Anthony Volpe were among the new teammates who’ve already reached out.

Stroman is physically ‘100 percent”

Last season with the Chicago Cubs, Stroman was 9-4 with a 2.28 ERA through June 20 (16 starts) when a hip problem flared up.

On his way back, a rib cage cartilage fracture effectively ended his season after July 31; he made four September appearances, totaling eight innings.

“Physically, I’m ready,’’ said Stroman, having already thrown “four-to-five’’ bullpen sessions in Tampa, Fla., residing 10 minutes from the Yankees spring training headquarters.

Manager Aaron Boone visited Stroman at his home before the signing, and Stroman described the ribcage fracture as fully healed.

Stroman last threw 200 innings in 2017, but he’s averaged 137 innings over the previous two seasons. His contract would become a $55 million, three-year deal if he pitches 140 innings in 2025.

“When I’m healthy, I would put myself up as one of the best pitchers in baseball,’’ said Stroman, adding, ‘I do think the best is still in me.

“I can’t wait and put the pinstripes on. It just couldn’t be a better fit at this point in my career.’’