In September, the Russian court told Mr Neustadt to return the two children. He lost an appeal against the decision on Wednesday.
Mrs Neustadt, who lives in Hendon, said that she was “delighted by the ruling” after campaigning for the last 11 months to bring her sons home.
Mr Neustadt has said he may appeal against the latest ruling.
He said: "We will finally reach some amicable solution based on compromises and not on possible actions that would be completely against the children's best interests."