Rivals Ferrari had written to the FIA asking for clarification about the legality of Vettel's lap four pass of Vergne, which appeared from on board video footage to have taken place under yellow flag conditions.
However, following clarification from the FIA that Vettel only passed Vergne after he had been shown a green flag, Ferrari said on Friday that the matter was now closed.
In a short statement issued on Red Bull's website, the reigning champions welcomed the matter coming to an end.
"We are pleased, but not surprised, that the FIA has confirmed there is no case to answer regarding the 2012 Brazilian Grand Prix," said the team.
"We are extremely proud of Sebastian's incredible achievement and his third historic title, which makes him the youngest ever triple world champion."
Red Bull faces a $3.26 million payout on Friday, meanwhile, as the deadline for entry fees for next year's Formula 1 world championship closes.
As part of the move to increase the FIA's revenue from Formula 1, teams have faced a dramatic increase in entry fees for the 2013 season.
The new structure replaces the flat 309,000 Euros fee with a sliding scale. Each team must now make a basic $500,000 payment, with the constructors' champions then paying $6000 per point scored and every other team paying an extra $5000 per point.
Although the rise in fees caused some controversy when it was introduced, FIA president Jean Todt said earlier this month that he believed the new system was much fairer.
"The smallest teams will pay less, as they will pay $500,000 - $800,000. So that is about six teams out of 12," he said. "The biggest teams with the biggest revenues will pay more.
"I feel in any democratic country you are paying your taxes depending on your income. So it will generate about 30 per cent more from this side."
F1 teams have already lodged their entries for next year, and made the $500,000 initial payment, but must now pay the full amount by the end of Friday.
The deadline will also likely make the fate of HRT clearer, with the outfit having already been given dispensation to delay its $500,000 when it lodged its original 2013 entry.