0404 GMT April 06, 2020
It means the 29-year-old from Belfast becomes the first Northern Ireland fighter to win a world title in two weight divisions, BBC reported.
Frampton was declared the clear winner by two of the judges, with the third seeing it as a draw.
It was a first defeat of the 27-year-old Mexican Santa Cruz's career.
"I wanted to be in a fight people would remember," said Frampton, having made good on his pre-fight promise to give fans a "shock".
His mentor and manager Barry McGuigan, who held the same title three decades ago, said: "This is one of the greatest nights of my life. It doesn't get much better than this."
It was Frampton's first pro bout at featherweight, having moved up a division after unifying the IBF and WBA super-bantamweight titles by beating England's Scott Quigg in Manchester in February.
The Belfast boxer, in his fifth world title fight, made the stronger start, rocking the champion on to the ropes with a series of heavy punches in the second round.
The classy Mexican, with a two-inch reach advantage, was clearly throwing more punches, but the more effective, cleaner work came from the challenger.
Frampton seemed to be building up a lead but Santa Cruz, who has held world titles at three weights, was on top in rounds six and seven of what seemed a close contest.
The Belfast man regained the initiative but was hit by a clean right-hand punch during the 10th and Santa Cruz finished strongly as he bid to sway the verdict.
One judge scored it a 114-114 draw but the others made Frampton the winner, 116-112 and 117-111.
It gave Frampton the belt McGuigan won more than 31 years earlier, when he memorably defeated Eusebio Pedroza at Loftus Road football stadium in London.
The new champion said he wanted to defend the title in his home city and did not rule out a rematch, although he also has IBF champion Lee Selby in his sights.
What they said
New WBA featherweight champion Carl Frampton: "I wanted to be in a fight people would remember.
"I wanted to be in with true champions like Leo Santa Cruz.
"This guy is a three-weight world champion. He is a true warrior and I respect him a hell of a lot.
"I would love to bring him to Belfast and show them an amazing fighter but I have a good relationship with Lee Selby's team. I want to be the best and be involved in big fights."
Defeated Leo Santa Cruz: "It was a pretty tough fight but now I want a rematch. I don't care where.
"He's a great champion and he's got a very difficult style. It's hard to forget your first loss but I will go back to the gym and get a rematch."