Cobo did not meet a deadline to challenge his three-year ban at the Court of Arbitration for Sport, the International Cycling Union said on Thursday.
The UCI said Cobo's suspension announced last month is confirmed, and he is stripped of results at the 2009 world championships and Vuelta, and the 2011 Vuelta which he won.
Froome was runner-up eight years ago and becomes the winner of his first Grand Tour title, and seventh overall.
"Better late than never!" Froome wrote on Thursday on his Twitter account. "The 2011 @lavuelta holds some very special memories for me."
Froome also becomes the first British winner of any of the major stage races - the Giro d'Italia, Tour de France, or Vuelta.
That honor was held by his former Sky teammate Bradley Wiggins, the 2012 Tour winner who rises from third to be runner-up at the 2011 Vuelta.
The 38-year-old Cobo is retired from racing. His doping ban was announced days after Froome suffered season-ending injuries crashing at the Dauphine race in France.
Froome's seventh Grand Tour lifted him to fourth overall, tied with Fausto Coppi, Miguel Indurain, and Alberto Contador. Eddy Merckx leads with 11.
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