BOSTON -- For maybe the only time in his life, Kenley Jansen was happy to turn a “Rocky” movie off.

It was about a week ago when Jansen received a phone call from his agent that revealed a two-year, $32 million agreement had been reached for him to close games for the Red Sox. That call swiftly trumped Sylvester Stallone’s inspirational film from over 40 years ago.

“It happened so quick,” Jansen said during Tuesday’s introductory press conference at Fenway Park. “I was excited. I couldn’t even finish watching my movie, because I’m coming to Boston.”

It was “Rocky II,” by the way, that Jansen, one of the most accomplished closers of his generation, was watching when he learned of his new baseball home.

This isn’t the first time Jansen will pitch for a storied franchise. He spent his first dozen big league seasons pitching for the Dodgers, with whom he recorded a 2.37 ERA over 701 games -- all in relief. His best season arguably came in 2017, when he finished fifth in the National League Cy Young Award voting after posting 41 saves, a 1.32 ERA, a 0.75 WHIP and a 109-to-7 K/BB ratio over 68 1/3 innings. Jansen was fitted for a World Series ring after Los Angeles won it all in 2020.

Jansen signed with the Braves prior to the 2022 season and led the NL in appearances (54) and saves (41), while averaging 12 strikeouts per nine innings.

The 35-year-old from Curaçao and possessor of a nasty cutter looks poised to continue the success he’s had thus far in his mid-30s. And now, he has the added adrenaline of doing it in Boston.

“It’s one of the historic organizations in baseball, and the weight that the name Red Sox carries, it just gets you excited, gets your adrenaline going,” Jansen said.

This was clearly a big deal for Jansen, given that he brought his wife and three young kids to the press conference. One of them charged into the room before the news gathering started and said, “Go Red Sox.”

Red Sox fans weren’t able to show that kind of enthusiasm much during a 78-84 season last year. But with Jansen on board to anchor what should be a much-improved bullpen, perhaps there will be more to cheer about in ’23.

Boston’s bullpen finished 26th in the Majors with a 4.59 ERA last year while converting just 39 of 67 save opportunities. Jansen, who ranks second among active relievers with 391 career saves (Craig Kimbrel, 394), is being brought along with Joely Rodríguez and Chris Martin to help improve those numbers. Manager Alex Cora also has last year’s breakout pitcher John Schreiber back in the fold, as well as Matt Barnes, the team’s longest-tenured player.

While chief baseball officer Chaim Bloom was determined to rebuild his bullpen piece by piece when the offseason began, he quickly identified Jansen as the most important target.

“What he’s accomplished to this point in his big league career speaks for itself,” said Bloom. “I don’t see how you could look at ways to improve your bullpen and not think about Kenley Jansen. … You talk about someone who has done this job for about as long as anybody has done it on the big stages. That’s something I think that will help everybody throughout our pitching staff.”

As Jansen addressed the media Tuesday, he was several stories above the bullpen he will warm up in next season. You could sense Jansen already envisioning what it will be like while he goes through his routine at Fenway prior to the ninth inning of a big game.

“I’ve got to be honest, it’s one of my favorite places to pitch,” he said. “When you come to Fenway, there’s the history behind it and you feel like a kid again. That’s what I felt when I was in other uniforms playing here. It’s a beautiful place to pitch. And the atmosphere, you see how intense the fans are.”

After being idle at Fenway in Games 1 and 2 of the 2018 World Series -- “They were winning the whole time,” Jansen remembered -- he got to pitch in Boston once for the Dodgers in ’19 and again for the Braves in ’22. He struck out four over 2 2/3 scoreless innings.

Before signing his name on the dotted line, Jansen said he spoke with Red Sox outfielder Kiké Hernández; the two were teammates in Los Angeles for six seasons. Jansen told Hernández that he “definitely” wanted to play in Boston.

“Next thing you know, here I am, sitting here and being a part of the organization,” Jansen said.

MLB.com’s Brian Murphy contributed to this story.