Wildenstein and seven other defendants had stood trial over claims that hundreds of millions in back taxes were unpaid because part of the family fortune had been hidden in offshore tax havens.
The case was based on accusations that Wildenstein and his nephew Alec undervalued the family fortune in tax returns for the family estate filed in 2002 and 2008 after Guy's father, renowned art dealer Daniel Wildenstein, died in Paris in 2001.
The defendants denied the charges.
After a long-running case the Paris court judge said there had been a “clear attempt" at concealment but the defendants were cleared because of weaknesses in both the investigation and French tax fraud legislation.
Judge Olivier Geron said it was impossible to return a guilty verdict. He told the court that the law must be applied the same way to "the powerful as to the poor”.
Lawyers for Wildenstein, 71, a friend of former French president Nicolas Sarkozy and the recipient of the Legion d’Honneur, previously said he denied “any form of guilt”.
His father Daniel was known to have owned numerous paintings by the likes of Monet, Renoir, Caravaggio, Picasso, Velazquez, and Rembrandt. The French tax authorities believe family trusts based in locations such as the Bahamas, Guernsey or the Cayman Islands, owned paintings valued at more than £850m.
The tax authorities are pursing the Wildenstein family in a separate civil court case for a reported £480m.