NEW YORK -- Limited to one inning in two years, Corey Kluber believes his ability will show with the New York Yankees.

"I consider myself to be healthy at this point. I'm not rehabbing anything or tending to any issues with anything lingering or anything like that," the right-hander said Thursday, a day after finalizing an $11 million, one-year contract. "I'm basically at a normal stage of my offseason right now."

Kluber completed his contract on the day AL batting champion DJ LeMahieu finished a $90 million, six-year contract to remain in pinstripes.

"It's no secret that I wanted to be back with the Yankees, I wanted to be back in New York. It was frustrating at times because it took so long," the relieved second baseman said. "I just think the whole free agent market in general was just slow."

A three-time All-Star who turns 35 on April 10, Kluber joins a new-look rotation that includes returnees Gerrit Cole, Deivi García and Jordan Montgomery along with Jameson Taillon, who was acquired from Pittsburgh last weekend after missing most of the past two seasons while recovering from Tommy John surgery.

Kluber won the 2014 and 2017 AL Cy Young Awards with Cleveland, going 56-20 and over the 2016-18 seasons. He was hit on the right forearm on May 1, 2019, by a comebacker off the bat of Miami's Brian Anderson and finished 2/3 with a 5.80 ERA in seven starts, then was traded to Texas. Kluber tore a muscle in his right shoulder in his Rangers debut on July 26, ending his season after one inning. The injury healed without surgery.

"That was extremely frustrating time for me, but I don't think I ever got down on myself," Kluber said. "I think that it's probably more of overcoming the mental aspect of it as opposed to physical ... getting out of that rehab mindset where you're trying to work through things or feel for things."

A three-time All-Star who is 98-58 with a 3.16 ERA in 10 seasons, Kluber has worked with Eric Cressey, who started last year as New York's director of player health and performance.

With age, Kluber has been prepared to make changes his his preparation.

"The biggest thing with those adjustments is listening to my body when something is telling you something, you got to listen to it," he said. "I think that there are times when you have to be smart and probably not try to have that mentality just to push through, push through, push through. I think that there's times when you're going to get in a little more treatment or maybe back off."

He already has prepared for reporting to the Yankees by shaving his beard to comply with a team rule.

"It feels a little bit naked but I'm getting used to it," Kluber said.

He is one of a few additions to the Yankees, who traded reliever Adam Ottavino to Boston and have a pending $2.5 million agreement with Darren O'Day, a bullpen switch that helps them remain below the $210 million luxury tax threshold. In addition, Luis Severino is expected to return at some point this season from Tommy John surgery last Feb. 27 and Domingo Germán is expected back from a domestic violence suspension that caused him to miss last season.

New York said goodbye to Masahiro Tanaka, who announced Thursday he had agreed to a two-year contract to return to Japan with the Pacific League's Tohoku Rakuten Golden Eagles.

LeMahieu joined the Yankees for 2019 and was thrilled to stay put and try to gain New York's first title since 2009.

"This is just a group I wanted to be a part of. This is this is an exciting group and we need to get over that hump," he said. "There's one goal with the Yankees and that's to win the World Series. And in my years we haven't been able to do it. So I wanted to be a Yankee, but I want to be part of this group even more. It's just an unbelievable group. I had guys reaching out all offseason: What's the holdup? What's going on? And I really appreciated that."

LeMahieu, 32, gets $15 million per season. The deal includes a full-no trade provision during the first two seasons and a limited no-trade provision starting after that giving him the right to block trades to five teams. He would have the right to approve a trade starting after the 2023 season, under the collective bargaining agreement, as a 10-year-veteran who has spent five years with his current club.

Also a three-time All-Star, LeMahieu had 10 homers and 27 RBI in the shortened 2020 season after hitting .327 with 26 homers and 102 RBI in his first year in New York. He doesn't think the Yankees fell short by much last season, when they lost a five-game Division Series to the eventual AL champion Rays.

"I think we ran into a really hot Tampa team. I thought we were better than they were," he said. "I think they just made a couple of plays that we didn't, and that was the bottom line and moving forward. We've got to make those plays, whatever it is. I just felt last year they just had our number and it was disappointing. And I really think we're going to get over the hump here."