Michael Bakwin asked the High Court to award him ownership rights on four canvasses, which were taken in 1978 and ended up with Sotheby's auction house.
The court granted a "delivery up" order so he could reclaim those pictures.
A fifth painting has been recovered, and Mr Bakwin's lawyer said the location of two others was known.
"We hope this is the last chapter in a fascinating saga," solicitor John Wardell told the judge, adding that further orders would be pursued to return those final two items.
He claimed it was now known that the thief - who was later shot dead over an unrelated debt - had left the paintings with a lawyer, Robert Mardirosian.
Several years afterwards, Mr Mardirosian transferred control of the paintings to a Panamanian firm, the Erie International Trading Company, which took them to Sotheby's in 2005.
The future of the artworks has remained in limbo since then, while the ownership rights were contested.
Separately, Mr Mardirosian was arrested at Boston airport two weeks ago and charged with the possession, concealment, storage and attempted sale of stolen goods.
He has been released on bail, the court heard, but has been told to give up his passport and was under a form of house arrest.
The seven pictures - all by French Expressionists - were originally acquired by Mr Bakwin's parents, who knew the artists in the 1920s.
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