"Putin's People: How the KGB Took Back Russia and Then Took On The West" alleges Russian President Vladimir Putin has overseen a vast exodus of ill-gotten money to spread influence abroad, including Abramovich's purchase of Chelsea in 2003.
Judge Amanda Tipples issued a ruling after Abramovich and Russian oil company Rosneft sued publisher HarperCollins and author Catherine Belton personally for libel, with their claims being heard together.
The judge said she agreed with Abramovich that several allegations in the book by the Financial Times' former Moscow correspondent were "defamatory of the claimant" and presented as statements of fact, not opinion.
The judge concluded that the critically acclaimed book alleged Abramovich "purchased Chelsea Football Club in 2003 at the direction of President Putin so that Russia could gain acceptance and influence in the UK".
HarperCollins said it was "carefully considering the judgement".
A spokesperson for Abramovich said "we welcome today's judgement" and called for the "false and defamatory claims about Mr. Abramovich to be corrected as soon as possible".
The book cited sources including exiled Russian billionaire Sergei Pugachev as alleging that Putin wanted Abramovich to buy Chelsea to increase Russian influence in the UK.
It also quoted a source close to Abramovich as denying this.
The judge ruled the passages' meaning to the reader is that Abramovich is "under the control of President Vladimir Putin" and "has had to make the fortune from his business empire available for the use of President Putin and his regime".
She said the book made several other defamatory claims concerning Abramovich, including over his alleged role as "cashier" for former Russian president Boris Yeltsin.
Tipples also ruled that one claim concerning Rosneft's purchase of an oil company was defamatory.
The rulings concerned only the judge's interpretation of how passages in the book would be interpreted by an "ordinary reasonable reader", not whether they were true.
This came after initial hearings in July when lawyers for the claimants presented the judge with lists of what they said were offending passages in the book.
Two other Russian oligarchs, Pyotr Aven and Mikhail Fridman, dropped legal claims after HarperCollins agreed to cut material from future editions.
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