Wheeler never has been an All-Star or led the league in any categories. But his addition could prove important over the course of the season.

“I was thrilled,’’ manager Terry Francona said yesterday of the signing. “Veteran guy who can throw an inning or multiple [innings], doesn’t shy away from big innings and he’s been through the American League East with Tampa and all that brings.

“Stand-up guy, great teammate. I think we’re really excited.’’

The Sox have their important bullpen roles established. Jonathan Papelbon is the closer with Jenks and Daniel Bard in place for the seventh and eighth innings. Wheeler can fill in the gaps.

The 33-year-old has the swing-and-miss stuff to face one batter in a tight spot. But he’s also capable of carrying a heavier load, having pitched two or more innings 20 times in the last five years.

Wheeler was used as a specialist against righthanded hitters by the Rays last season. Francona said the Sox don’t plan to follow that model.

“We certainly just don’t want to pigeonhole him into pitching against righthanders because he had the ability to get out both,’’ the manager said.

Having Wheeler should enable Francona to survive those days when Bard, Jenks, or Papelbon needs rest.

“It’s important to the health of the bullpen. You need multiple guys who can go out and get the job done,’’ Wheeler said. “That’s just going to make us stronger through the course of the year.’’

A Rhode Island native who grew up rooting for the Sox, Wheeler is excited about pitching in Boston after stints with the Mets, Astros, and Rays. But what means more is a chance to win.

“At this stage of my career, that’s important to me,’’ he said.

Wheeler also has the advantage of having so much experience pitching in the division.

“I think it’s big. Just kind of knowing what it’s like on a daily basis. It’s a grind,’’ he said. “It’s the best division in baseball, that’s no secret obviously. I enjoy that part of it. Every day you have to come ready to play and pitch. You can’t lose your focus for a second because nothing good can happen.’’

Wheeler was one of six relievers who left Tampa Bay as free agents. He, Randy Choate, Grant Balfour, Joaquin Benoit, Chad Qualls, and Rafael Soriano signed deals totaling $67.65 million.

“That’s just the way it is and that’s just the way it was. The owner [Stu Sternberg] came out and said they overextended themselves for a couple of years in a row so now they were going to have to cut payroll and that’s what they did,’’ Wheeler said.

Candid on Cameron Mike Cameron has yet to arrive in camp. But the veteran outfielder told Francona that he has recovered from extensive surgery to repair a hernia and groin tear last August.

“He’s good; he feels terrific. The idea is to keep him that way,’’ Francona said. “I’m actually kind of looking forward to seeing him. He’s so excited about how he feels. Last year was tough for him.’’

Cameron, 38, was injured in spring training last season but played in 48 games before having surgery. He starts the season as the fourth outfielder but will see playing time in right field. He also can play center and left field or be the DH.

“Oh yeah, especially with J.D. [Drew] being lefthanded. You’ll see him in spring training playing a lot of right field,’’ Francona said.

Drew hit only .208 against lefthanders last season and is already battling a sore upper left hamstring. Cameron has a career .866 OPS against lefties.

Putting a stop to it Like many teams, the Sox conduct physical testing in camp to get a more accurate read of their players. In recent years, that has included a timed 300-yard shuttle run.

The run has been canceled this year in the interest of keeping players healthy.

“We felt like with the guys coming off some injuries and the ways guys compete, we just decided to do everything inside,’’ Francona said. “We’ll do the shuttle as a form of conditioning this week, but not as a form of testing. We felt like we were putting guys in awkward positions.’’

Getting started Pitchers and catchers will meet with the coaching staff at 9 a.m. today before taking the field. Position players who are here early will work out an hour later . . . Righthander Robert Coello, designated for assignment last week, soon may be traded . . . Shortstop Jose Iglesias soon will be reunited with his father, who was cleared to leave Cuba and is in Mexico en route to the United States. “It’s going to be nice to have him around,’’ Iglesias said . . . Jon Lester, a cancer survivor, was one of the judges picked by Major League Baseball to select honorary bat girls to attend games on Mother’s Day. The program will help raise awareness and support victims of breast cancer. Go to www.honorarybatgirl.com for more information.

Peter Abraham can be reached at pabraham@globe.com. Follow him on Twitter @peteabe.