Sir Chris Hohn, 48, and 49-year-old Jamie Cooper-Hohn had fought over who should get what in one of the biggest divorce fights seen in an English court.
He said she should get a quarter of his wealth, but she had argued she should get half because the wealth was created as a result of their "partnership".
Last month, Mrs Justice Roberts, who had analysed evidence at a hearing in the Family Division of the High Court in London, said she had awarded Mrs Cooper-Hohn £337 million.
Her calculations on the exact size of the fortune, and the exact percentage Mrs Cooper-Hohn would get, emerged today when she delivered a detailed ruling.
The judge concluded that Sir Chris had assets worth about £1 billion, saying he had been the "generating force" behind the creation of the fortune. She said he was a "financial genius".
The award is thought to be the biggest of its kind made by a judge in England. Legal experts said it is "certainly" one of the biggest payouts to be pocketed by an estranged wife.
However, lawyers for Mrs Cooper-Hohn have indicated that they might appeal because the payout is not big enough.
Sir Chris and Mrs Cooper-Hohn, who separated after being married for more than 15 years, had disagreed over how their fortune should be divided.
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