Spaniard Cobo, now retired, was removed as the overall winner and handed a three-year ban after an investigation based on irregularities in his biological passport found that he had used a banned substance.
The decision meant that Froome, who finished second to Cobo, was handed the victory with his then Team Sky teammate, Bradley Wiggins moving to second and Bauke Mollema, riding for Rabobank, third.
"To be named the winner eight years on does feel a bit strange on the one hand, but at the same time it's a really special one to add to my palmares", Froome said.
The Kenyan Born Briton now holds seven Grand Tour victories, four from the Tour de France (2013, 2015, 2016, 2017), two at the Vuelta (2011, 2017) and one Giro d'Italia (2018).
"This title, this red jersey really does mean a lot to me", he said. "That race back in 2011 was incredibly special for me. It was the race that I first started to believe in myself as a Grand Tour contender.
"It would've been so different had I actually won it back then. Being able to stand on that podium in Madrid and soak up the feeling of winning my first Grand Tour and being the first British rider to ever win a Grand Tour, that would've been an amazing feeling."
Froome is currently recovering from a crash at the Criterium du Dauphine which left him with femur, neck, ribs and hip fractures.