Sellers 'delighted'
The intricately designed eggs, about 13cm (5in) tall and made of precious metals and gems, include the Coronation Egg, which features the coach that Empress Alexandra rode into Moscow in 1897.
The religious, spiritual and emotional content captured by these Faberge eggs touches upon the soul of the Russian people
Victor Vekselberg
The Forbes publishing family said it was "delighted that the advent of a new era in Russia [had] made possible the return of these extraordinary objects".
Mr Vekselberg said the Forbes collection represented "perhaps the most significant example of our cultural heritage outside Russia".
He told the BBC that the eggs would be brought back from the US by April.
He described them as priceless and said he was overjoyed to be returning such a significant collection to Russia.
"The religious, spiritual and emotional content captured by these Faberge eggs touches upon the soul of the Russian people," he said.
It was not immediately clear what the industrialist, who is chairman of the board of directors of investment and business development company Renova, planned to do with the collection.
However, Russia's most powerful museums have begun staking their claims to them.