Joshua retained his IBF heavyweight title and claimed the vacant WBA and IBO straps with an 11th-round stoppage of Klitschko in front of 90,000 fans at Wembley.
The Briton sent Klitschko to the canvas in the fifth round but appeared set for defeat after the Ukrainian knocked him down a round later.
However, the unbeaten Joshua recovered and hit Klitschko with a penultimate-round barrage that sent the 41-year-old to the deck twice more before the referee called a halt to an enthralling contest.
And Tyson believes Joshua is the type of fighter who elevates boxing to the next level.
He said at a media conference ahead of a launch gala for his boxing fitness franchise - the Mike Tyson Academy: "We have a new heavyweight champion that's pretty exciting right now. If he continues to be that way, the sky's the limit for him.
"Just that one fight changed boxing and that's what fighting needs.
"Floyd [Mayweather] is making a lot of money and we got a lot of little guys fighting, but what they want to see is a heavyweight fight, [and] a heavyweight that knows how to fight, like Joshua.
"That's what makes boxing big, the heavyweights make boxing big. The other guys can make some money, but they're not making the sport big."