DeGale's medal was Team GB's third in boxing - after bronzes for super-heavyweight David Price and light-heavyweight Tony Jeffries - meaning they exceeded UK Sport's target of two medals of any colour.
DeGale, who was ranked as one of the outsiders for gold in Beijing, sank to his knees at the end of the bout before parading around the ring with the Union Flag draped over his shoulders.
"It was not that good, but it was strong," he said. "I just wanted to win. He was pretending that I was holding on to him - and then he bit me in the first round.
"He was tough, horrible and strong throughout the bout. But I'm Olympic champion, it's unbelievable."
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Video - DeGale delight at middleweight gold
Correa was trying to emulate his father, who won Olympic gold at welterweight in Munich in 1972, but struggled to cope with DeGale's counterpunching.
He closed the deficit in the third round, winning it 6-2, as he lured DeGale into a streetfight and the Hammersmith fighter was penalised for holding.
It set up a wild finish with the Cuban digging in and DeGale responding with shots of his own to just about maintain his advantage in a thrilling finale.
"I'm not happy with the way the judges scored the fight but that's it," said Correa. "He won and he's got the gold medal."
Britain's boxing coach Terry Edwards was delighted with the victory although he did think the referee "lost the plot" during the contest.
"The last minute was painful," he told BBC Sport. "It was not the greatest bout but you have to do what you have to do in an Olympic final."
Edwards, who was appointed by UK Sport, was again critical of the Amateur Boxing Association, which he believes is trying to undermine him.
Video - DeGale and Jefferies skip-off
"The return of medals in Beijing is down to UK Sport and we have delivered, so you deliver for us," he said.
On a more positive note, Mayor of London Boris Johnson was quick to send his congratulations to DeGale.
"Our man is a great ambassador for our city and is further tribute to the inspirational performance of team GB," said Johnson.
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