Cobo took a 13-second lead over Team Sky’s Chris Froome into the finale and defended it during Sunday’s 21st and final stage, a relatively flat 95.6km race from Circuito del Jarama to Madrid.
Peter Sagan (Liquigas-Cannondale) won the finale ahead of Daniele Bennati (Leopard-Trek) and Alessandro Petacchi (Lampre-ISD).
It was Sagan’s third stage win and helped make amends for teammate Vincenzo Nibali failing to defend his crown from last year.
The 30-year-old Cobo began the race with the job of riding in support of former champion Denis Menchov and Tour de France winner Carlos Sastre and could not hide his joy at the finish line.
“I thought I’d be working for Denis and Carlos throughout the Vuelta, and I’ve ended up winning,” said Cobo.
“It’s incredible, I would never have entertained such thoughts before the start of the race.”
Froome had become Cobo’s main challenger in the last days of the three-week epic after Sky teammate Bradley Wiggins had dropped steadily out of contention in the final week.
However, Froome was unable to overturn his slim deficit during the closing stages. He finished second overall at 13 seconds with teammate Wiggins third at 1:39.
“The race was over at the top of Pena Cabarga (on stage 17),” said Froome. “The gap between Cobo and myself remained the same after that. I’m happy anyway.
“Three weeks ago, I couldn’t envisage such a result and I believe it’s the beginning of great stuff. For the first time I got the opportunity to ride a grand tour in the best conditions and I took my chance.”
As for Cobo, it was the biggest win of his career, which has been spent as a loyal domestique in the mountains for more heralded teammates. Until Sunday’s win the Spaniard’s best result at the Vuelta was a 10th place in 2009, when he won the race’s 19th stage.
This time around, he took over the race leader’s red jersey from Wiggins on stage 15 when an epic climb to the Angliru — one of the most notoriously difficult climbs in cycling — saw him leave the Englishman in his dust.
Wiggins, who crashed out of July’s Tour de France with a broken elbow, could not hide his disappointment at finishing third at the Vuelta.
“I put pressure on myself during three weeks. I’ve seen myself as the winner. I’ve truly believed that I was going to win, that’s why I’m not satisfied,” he said.
“I’m speaking negatively but there’s some positive as well. Nine weeks ago, I broke my collarbone and I would have laughed if anyone told me that I was going to finish third of the Vuelta after that.”
David Moncoutie gave his Cofidis team a huge boost by winning the race’s King of the Mountains jersey for the fourth year in a row.
Bauke Mollema (Rabobank) took the green jersey for the sprinters’ points competition alongside an impressive fourth-place finish.