High-flying Vince Carter is flying straight into the Hall of Fame.

The Nets legend was announced Saturday as among 13 inductees into the Naismith Basketball Hall of Fame for the Class of 2024.

Though the announcement came in Glendale, Ariz., at the Final Four, the call that changed Carter’s life came April 1 — and had him afraid it was a prank.

“It was April 1, so April Fools’ Day. So, just curious. So when I received the phone call, I stepped outside. I needed all the fresh air I could get, just in case,” Carter said at a press conference. “Grant Hill is a friend of mine, and he was trying to tell his story of that phone call, and he was trying to tell the story of what it was like for him. Going forward, I can share this story with anyone: You can’t put it in words. You can’t put it in words just because of the magnitude and the significance.

“You think about the people that are in there. … It’s mind blowing for me. And I enjoy playing the game of basketball every day, and I’m just overjoyed now that my career is over, like somebody said, the cherry on top: This is it.”

Carter, who told The Post he’d never actually been inside the Hall of Fame before, will get to step through those doors and be enshrined on Aug. 16-17 along with a Class of 2024 that includes Chauncey Billups.

He’ll join former Nets teammate Jason Kidd, as well as cousin and former Raptors teammate Tracy McGrady, in receiving the highest honor that the sport can give.

“Thank you. Like Chauncey and everyone’s gonna say, this is truly an honor,” Carter said at a press conference in Arizona. “You grow up and you just develop a love for the game of basketball. You want to be the best version of yourself each and every day, whether it’s on or off the court.

“I have so many heroes that have been on the stage and get to be here, and I have a family member in Tracy McGrady who’s a Hall of Famer. So, to watch it, to hear about it, to hear your friends saying, ‘Oh, you deserve to be in it.’ It’s all well and good until you get that phone call. Like everyone here, the reality is it’s better than you can imagine, and it’s just an honor to be a part of this class.”

Renowned for his high-flying dunks that earned him the nickname “Vinsanity,” Carter was an eight-time All-Star in his 22 seasons from 1998-2020.

He’s still the only NBA player in history to play in four different decades.

Carter, who has broadcast several Brooklyn games for YES Network this year, holds the Nets’ single-season franchise scoring record in addition to the Raptors’ mark.

Of his 25,728 career points, 8,834 of them came in a New Jersey uniform spread over five seasons.

He was an iron man, missing just 11 games in those five seasons and the Nets losing all of them.

For Carter, this has been an emotional capstone on his career.

“For me, it’s emotional because I have a great appreciation for it,” Carter told ESPN. “That’s where the emotions come from me, because yes, I played the game and I’ve had [people say] ‘Oh, of course you are.’ But you know, until you receive that call, the reality is what was bliss for me. I was like, OK, it is real. OK and now you’re here. But I just needed to hear it for me to believe it, I think.

“And my appreciation for the Hall of Fame, my cousin, watching T-Mac get in, I was like the proud cousin in 2017. It just made me proud, and my heart was beating at that time. So for a very long time some of the friends that I’ve seen go in and that I played against are in there. And I was like wow, what an honor for the elite that are in there. I get a chance to be a part of that. I mean, unreal.”