After being outclassed by Briton Froome at the Tour de France, the 26-year-old struck back to become his country's first Vuelta winner since Lucho Herrera in 1987.
Quintana, who led from stage 10 onwards, adds the victory to his win in the Giro two years ago, which was also the last time his team Movistar won a three-week tour.
Magnus Cort Nielsen of Orica-BikeExchange won the final bunch sprint in Madrid ahead of Daniele Bennati and Gianni Meersman, but this was Quintana's day.
Cheered on by many of his compatriots lining the Madrid streets, Quintana said it had been a "dream" victory.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"It felt like half of Colombia were here," he said. "It was spectacular. I've been fighting so many times to win La Vuelta and now finally we've done it.
"This morning in my head I was a winner but I knew I had to cross the line and until you cross it you can't say you are champion."
Froome, 31, applauded Quintana over the line on Saturday after he had successfully fought off his attacks in the final and decisive day in the mountains around Benidorm.
Sunday's stage was processional and even saw Froome and Quintana share a glass of champagne.
Froome's chances of becoming the first rider to win the Tour de France and Vuelta back-to-back for the first time in 38 years took a hammer blow on stage 15 last Sunday when he missed a break and Quintana grabbed two minutes 43 seconds to add to the lead he had already established.
It was a rare crack in the Team Sky machine as Froome's team mates, for once, failed to help him. Michal Kwiatkowski abandoned the race in the first week and Froome's seven remaining team mates were all among the riders permitted to continue after missing the time limit.
Although he clawed back more than two minutes in Friday's individual time trial the damage had been done.
Froome finished second for the third time, one minute 23 seconds behind Quintana.
While victory tasted sweet for Quintana the goal, he said, was now beating Froome at next year's Tour de France.
"Froome is strongly protected but we have to try to take advantage of all kinds of different situations," he said. "Above all, winning here has given us the confidence to try."
"He is the greatest rival there is at the moment. He made me suffer at the Tour and here I have won."
Having made the podium three times in the Tour de France, this victory will allow Quintana to believe he can finally oust Froome next year, although Team Sky will be much stronger after their disappointing showing here.
(Editing by Martyn Herman)
