Alex Bregman, who starred at third base for the Astros, has agreed to a deal with the Red Sox, likely to play second base. Kevin M. Cox/Associated Press

FORT MYERS, Fla. — Shortly after 10 p.m. Wednesday, the Red Sox awoke from their hibernation.

What began as a promising offseason with upgrades to the pitching staff stalled when it came to finding the right-handed bat they so obviously needed.

They sat idle as the free-agent market was nearly picked clean, and as spring training began, it seemed the Red Sox were content to get by with what they had.

Their choices appeared narrowed to either Alex Bregman or Nolan Arenado, and with Bregman reportedly looking for a six-year commitment as recently as Wednesday afternoon, the expectation throughout the industry was that a trade with the Cardinals to acquire Arenado seemed the far likelier option.

Until it wasn’t. Until the Red Sox, who stood their ground and refused to hand out a six-year deal, got Bregman with a different strategy: short-term, but big money.

The Red Sox and Bregman, a major league source confirmed, have an agreement in place for three years and $120 million with opt-outs after each of the first two seasons and some of the money deferred.

It’s a big swing for the Red Sox. The $40 million average annual value is the largest in franchise history, eclipsing the $31.35 million handed out a few winters ago as part of a mega-extension for Rafael Devers. Since David Price, this is only the third nine-figure deal the Red Sox have issued, following the deals signed by J.D. Martinez (five years, $110 million) and shortstop Trevor Story (six years, $140 million).

The deal could last only a year, or two, but for the time being, it addresses the club’s most pressing need. It provides the lineup with some righty sock. It gives the team a Gold Glove-winning infielder, albeit likely at a position (second base) he’s played for just 32 innings in the big leagues. And it infuses the club with a veteran leader and winner who has gone to the postseason every year since 2017.

Beyond limiting the Red Sox’ exposure for a player who turns 31 next month, it also limits the pressure that would have been placed upon either Vaughn Grissom or Kristian Campbell.

Assuming that the Red Sox made this move with the idea of Bregman playing second base, the Red Sox now have an experienced middle-infield combination.

Until Wednesday night, either Grissom or Campbell was likely to be the team’s starting second baseman on March 27 in Arlington, Texas. That would have represented plenty of risk — Grissom is unproven at the major league level, and talented as he is, Campbell has just five weeks of experience at Triple A.

Red Sox Manager Alex Cora on Wednesday afternoon spoke about the need to improve the team’s infield defense, and no matter where he plays, Bregman will advance that cause.

Mostly, however, Bregman dramatically upgrades the everyday lineup. While it’s true that his OPS has dipped in each of the past two seasons, the opportunity to play half his games at Fenway Park could revitalize Bregman as a hitter.

Alex Bregman has a .375 batting average and 15 RBI in 21 regular season games at Fenway Park. Kevin M. Cox/Associated Press

He has a short, power stroke, with the ability to pull the ball in the air. That new hitting environment, as well as being surrounded by Jarren Duran, Devers and Triston Casas could invigorate Bregman. In his regular season career, Bregman has gone 30 for 80 (.375) at Fenway Park with seven homers, nine doubles and 15 RBI, with a .490 on-base percentage and a .750 slugging percentages.

Somewhat tougher to quantify is what this signing means in terms of an intangible like fan belief. Following a quiet stretch in which they bolstered the pitching staff with the acquisition of Garrett Crochet, Walker Buehler and Aroldis Chapman, the Red Sox offseason sputtered.

When president/CEO Sam Kennedy and chief baseball officer Craig Breslow praised the organization’s urgency in recent comments, it sounded hollow. With nothing but a backup catcher (Blake Sabol) added since Christmas, the self-congratulatory nature of the remarks was off-putting.

Now, the Red Sox are allowed to take their bows, and in so doing, have earned back the trust of a demoralized fan base.

Credit, too, to Breslow, who clearly won the staring contest with Bregman’s agent, Scott Boras. Just as clearly, Bregman far preferred Boston to other alternatives — he turned down six years and $171 million from the Detroit Tigers and $120 million over four years from the Chicago Cubs.

The Sox’ offer — $120 million over three years — bought them Bregman. But in winning back the disillusioned fans who had been alienated, it also brought them the credibility they had squandered.