GLENDALE, Ariz. — The possibility was real.

Clayton Kershaw acknowledged Sunday that all the offseason speculation about him possibly leaving the Dodgers to sign with his hometown team, the Texas Rangers, this winter was accurate. That pull was strong and he and his wife, Ellen, thought long and hard about it before making the decision to re-sign with the Dodgers, returning to the team for which he has built a Hall of Fame legacy.

Kershaw’s one-year, $17.5 million contract became official Sunday.

“The lockout was honestly a blessing for my wife and I — just selfishly to be able to make sure my elbow was okay,” Kershaw said after working out at Camelback Ranch Sunday. “We didn’t want to make any decisions without knowing that I was going to be 100 percent.

“Once I got healthy, it was no secret. I was either going to go play in Texas or stay here. That was a hard phone call to tell CY (Rangers GM Chris Young). I’m a good friend of CY. I think the world of him and I think he’s going to do great things with Texas. But at the end of the day I want to be here and I want to win a World Series. I think the Dodgers give me the best chance to do that and I’m excited to be back.”

The Kershaw family grew during the lockout with the birth of their fourth child (and third son) in December. Kershaw acknowledged “the draw of being home more and keeping them in school was big.” But the draw of being with a championship contender remained bigger.

“Ellen was on board. She wanted to do this again,” Kershaw said.

Signing only a one-year deal means Kershaw will have the option of re-visiting his decision again next winter. With his 34th birthday later this month, Kershaw might have reached the point in his career where the calculus will change from year to year.

“Every year is going to be different. I don’t know,” he said. “But this year, this was the right call and I’ll figure it out next season.”

Kershaw said he never considered retirement “unless my elbow was bad.” But the health of his left elbow was an unknown factor for much of this winter.

After missing two months with forearm/elbow pain, Kershaw returned to pitch in September but left the mound at Dodger Stadium in the second inning of his start on Oct. 1 with renewed pain in his elbow. He received a platelet-rich plasma injection in the joint shortly after and did not pick up a ball again until January.

There has been steady progress ever since, Kershaw said, and he has been throwing off a mound in preparation for spring training. He is scheduled to throw live batting practice to hitters during Monday’s workout.

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“I feel 100 percent health-wise,” he said. “I wasn’t really sure how it was gong to react.

“It was a process. As I started throwing in January, I started feeling better and better. Every day I was throwing a little bit more and I wasn’t as sore. Then I started throwing off the mound a little bit more and kept bouncing back. Just kind of one day it was, ‘I’m healthy.’”

Dodgers president of baseball operations Andrew Friedman said Kershaw was his first call after the lockout was settled on Thursday. They quickly reached agreement on the one-year contract.

Kershaw said he “did a bunch of MRIs today and yesterday” and feels as confident as he can that the elbow issue has been resolved.

“I feel great,” he said. “Obviously you can’t predict the future. But I didn’t want to come back if I thought there was going to be a chance that I could get hurt. Obviously, health is unpredictable at times. But I’d rather not play than get paid and be hurt, honestly, at this point in my career.

“I wouldn’t come back if I didn’t think I was healthy. I wouldn’t come back if I didn’t think I could pitch a full season and be ready to go. That’s what I’m here to do.”