Matt Bush was a world away from Yankee Stadium during the more than three years he spent in a Florida prison for his third DUI conviction, a hit-and-run that nearly killed a 72-year-old motorcyclist during 2012 spring training.

But he made it to the Bronx Wednesday as a relief pitcher for the Texas Rangers, less than seven weeks after his big-league debut on May 13. Bush, 30, a San Diego native, was drafted first overall by the Padres in 2004, but struggled in the minor leagues amid injuries, alcoholism and legal troubles. He is 2-1 this season with a 3.10 ERA in 20 1/3 innings and said he’s working hard to keep his life on track.

On Wednesday, he relieved against the Yankees with one out in the eighth inning. He got Chase Headley to fly out and struck out Aaron Hicks to end the inning. But he allowed a single and a walk in the ninth before being pulled and was charged with two runs in the Yankees’ 9-7 victory.

“It’s amazing,” Bush said of his first time in New York, aside from a trip to Cooperstown at age 12. “I’ve always dreamed of one day being able to play a baseball game in Yankee Stadium. I remember growing up and watching the Yankees and the playoffs and the World Series and everything and thinking, ‘man, that’s the place to play a baseball game. That would be amazing.’

“It goes to show that when you put things in order and lean on God and stay on the right path, amazing things can happen. I’m living proof of that right now, just staying the course and doing what I need to do. I’ve been blessed and fortunate to have the talent . . . to be able to go through everything I’ve been through and to be in Yankee Stadium, I’m just trying to soak it all in.”

Bush said he played softball when he was in prison and his arm strength never deteriorated. He added that he throws in the mid-to-high 90s and became baseball-ready soon after he was released from prison.

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Rangers manager Jeff Banister said the organization saw Bush in spring training multiple times and signed him because of his arm and potential — and he hasn’t disappointed yet.

“Big fastball, changeup, threw a lot of strikes, was overpowering,” Banister said. “Since he’s come up with us he’s added the slider and he’s shown exactly the same thing that he showed us in spring training.

“He has been successful. He’s gotten a lot better against lefthanders. Love the intensity. This is a guy with talent. There’s an opportunity to give a guy a second chance.”

It’s an opportunity Bush doesn’t plan on squandering.

“Now that I’ve been able to set aside my off-the-field issues with alcoholism, I’m here and hopefully here to stay,” Bush said. “The past is the past, I’ve been through what I’ve been through, I’ve learned from all my mistakes and I know what I want to get out of life now. I think it’s showing with the success I’ve been able to have.”