A host of fellow stars descended on the Italian city’s canals for the union between the film world’s most eligible bachelor, 53, and Ms Alamuddin, 36.
The ceremony was celebrated in a hotel overlooking the famous Grand Canal.
Clooney’s agent broke the news to journalists in a brief statement.
According to AP news agency, that will be the only communication on the wedding.
Clooney and his friends had sipped champagne before gliding up the Grand Canal last Saturday evening to the luxury Aman Hotel, waving to hundreds of well-wishers.
Guests include Cindy Crawford, Bill Murray, Matt Damon and the U2 singer Bono.
Clooney’s boat was momentarily blocked by a passing cruise liner and then by a water bus, giving time for dozens of boats carrying photographers to catch up, AP writes.
A police boat swerved in vain to try to keep the paparazzi away.
Ms Alamuddin was last seen publicly last Friday riding in a water taxi down the Grand Canal with Clooney’s arm round her.
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