The United States Attorney's Office for the Eastern District of New York accuses Rocha of demanding and taking bribes of $150,000 in connection with the sale of marketing rights to World Cup qualifying games.
In all, 14 people were indicted by U.S. authorities on May 27, throwing soccer's governing body FIFA into the worst crisis in its 111-year history.
Following the arrests, Swiss authorities began their own investigation and last month opened criminal proceedings against FIFA president Sepp Blatter for criminal mismanagement.
He was then banned for 90 days by FIFA's own ethics committee along with Michel Platini, the head of European soccer's governing body and the favourite to succeed him in next year's FIFA election.
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Rocha, a former FIFA development officer, has 30 days to appeal the extradition approval, the FOJ said, adding that it had given priority to the U.S. request over a similar one from Nicaragua.
The FOJ said that, according to the extradition request,
"Rocha massively influenced the competitive situation and distorted the market for media rights in connection with the World Cup qualifying matches."
It added: "Other sports marketing companies were placed at a disadvantage, and the football federation concerned was prevented from negotiating more favourable marketing agreements.
"In Switzerland, such conduct would be deemed unfair practices under the Federal Act on Unfair Competition."
The FOJ said it had given priority to the U.S. request because the U.S. authorities had been conducting wide-ranging criminal proceedings against a number of individuals for some time.
"These individuals are already in the USA, or are to be extradited to the USA. Most of the evidence and witnesses are also located in the USA," it said.
The Nicaraguan charges, on the other hand, were against a single individual and "do not permit an overall evaluation of the facts at hand," the FOJ said.
Of the seven arrested in Zurich, only former FIFA Vice President Jeffrey Webb agreed in July to be extradited to New York, where he has pleaded not guilty.
The other six remain in Switzerland, though the FOJ has also approved U.S. extradition requests for Uruguay's Eugenio Figueredo, Venezuelan Rafael Esquivel, Eduardo Li of Costa Rica and Costas Takkas, a British citizen.
An extradition request is still pending for Jose Maria Marin, a former head of the Brazilian Football Confederation (CBF).
(Reporting by John Miller; Writing by Brian Homewood in Nyon, Switzerland; Editing by Richard Balmforth)
