By Leonardo Goy and Roberta Vilas Boas

SAO PAULO (Reuters) - Brazil opened two of its busiest airports to private investors on Friday, awarding $9 billion worth of contracts in a hotly contested auction as the country overhauls crowded terminals ahead of the 2014 World Cup and 2016 Olympics.

The concessions, in Rio de Janeiro and Belo Horizonte, mean private operators will be running the international airports in both World Cup host cities next year, but there will be little time for their investments ahead of the tournament in June.

Local contractors and foreign airport operators won the two concessions for a combined 20.8 billion reais ($9 billion), paying a premium of more than 250 percent over minimum bids as they hope to cash in on a recent boom in Brazilian air travel.

It was a welcome victory for President Dilma Rousseff, who has struggled to restore credibility with the private sector as economic growth slumps and investors complain of a heavy-handed approach to concessions in the power industry and elsewhere.

"The result of the auction was exceptional. It proves the country is on steady footing and it's attracting great interest from foreign investors," said Wellington Moreira Franco, Rousseff's civil aviation secretary.

Brazilian conglomerate Odebrecht and Singapore's Changi Airport Group will have two years to expand Rio's Galeão airport before the city hosts the 2016 Olympics, sprucing up an underwhelming international gateway to Brazil's postcard city.

Brazil's CCR SA (CCRO3.SA) and the operators of airports in Zurich and Munich edged out builder Queiroz Galvão and Spain's Ferrovial (FER.MC) for rights to Confins airport in Belo Horizonte in bidding that lifted their offer 30 percent.

Airports have been the most appealing aspect of Rousseff's plan to privatize some 200 billion reais of infrastructure projects, including expansion of Brazil's notoriously clogged roads and seaports.

Rousseff pitched her program last year as a shot in the arm for an ailing economy, but some investors have balked at what they call unrealistic projections and intimidating red tape. The government had to call off auctions for highways and high-speed trains this year because of weak private-sector interest.

After promising a dozen rail concessions by February 2014, the government is now aiming for just three in the first half of next year, according to political analyst Jefferson Finch of Eurasia Group. Government officials have been silent on the auction of four public ports expected this year, he added.

Interest in Brazil's airports highlights the appetite for profitable projects if investors are convinced of a fair deal, but that demand has not yet rubbed off on other auctions.