The deal includes an opt-out after the fourth season, sources said.
Story, 29, could be moved to second base alongside Red Sox shortstop Xander Bogaerts. At the major league level, Story has never played a position other than shortstop, where he ranked among the majors' best in 2019 with plus-18 outs above average and was a National League Gold Glove finalist.
Bogaerts, the Red Sox's primary shortstop for the past seven seasons, said Sunday that it would be great to have Story join the Red Sox, calling him one of "my top five shortstops that I like." But Bogaerts added that the move doesn't make him worry about his position.
"I play baseball. I'm not at the front office or [involved in] making those type of decisions," Bogaerts said, noting that he hopes to stay at shortstop. "But he is a great player. So that's all I got to say. If you brought in someone like that, it will help out the team."
Enrique Hernandez, who has played multiple positions in his career and at times filled in at second for the Sox last season, said he hoped Story's addition would allow him to settle down in center field. He also understood what Story would go through with a possible position switch.
"When I switched over to second, it almost felt like I was playing in front of a mirror," Hernandez said. "Everything looked sideways, backward, whatever you want to call it. It was just weird. And especially with [Story], he's been playing there his whole life. It might be a little different at first.
"But again, I've always said that if you can play shortstop, you can play anywhere. And I've seen him play enough to know that he's incredibly athletic, he's gifted. So I don't doubt one bit that he's going to be able to transition smoothly to second base and help us win some ballgames and help us get to October and deep into October."
Story hit a crowded free-agent field -- alongside fellow shortstops Carlos Correa, Marcus Semien, Javier Baez and Corey Seager -- with a résumé featuring two All-Star Games, two Silver Slugger awards and MVP votes during the 2018, 2019 and 2020 seasons.
Red Sox right-hander Nathan Eovaldi said Story's addition would bring a spark to the clubhouse.
"It shows us the front office ... we know that they want to want to win ... but then to add another big piece to the organization like that would be huge," Eovaldi said. "And the energy and everything that he brings to the team, seeing him across the field, it's exciting watching him play. And to have him back there behind you, especially for me while I'm pitching, and then scoring runs for us. ... Our lineup is already extremely talented, and to add another piece like that, it's only going to make us better."
The concern with any player who built his career with the Colorado Rockies is that career numbers are skewed by playing half of his games at Coors Field. Story's batting average and on-base percentage are 60 points lower on the road, his slugging percentage 160 points lower, and his wRC+ 27 points lower. In recent history, Nolan Arenado, DJ LeMahieu and Troy Tulowitzki all became markedly better road hitters with worse home splits after leaving Colorado, though three players is hardly a definitive sample size.
Story has shown big power in the past, hitting 37 homers in 2018, 35 in 2019, 11 during the pandemic-shortened 2020 season, and 24 in 2021. In 2019, Story reached 100 career homers in 448 games, becoming the fastest shortstop to ever do so. In his six-year tenure with Colorado, he solidified himself as one of the best players in franchise history, ranking in the top 10 in homers, doubles, triples and stolen bases. He also tied for 14th in the majors in steals last season with 20.
USA Today first reported on the Red Sox's agreement with Story.
ESPN's Marly Rivera and Joon Lee contributed to this report.