The sentence, read out in court by judge Marco Tremolada, comes more than three years after the trial first began and after a total of 74 hearings. He said the companies and defendants had been acquitted as there was no case to answer.
Rulings in Italy can be appealed and only become enforceable once they are final.
The long-running case revolved around the $1.3 billion purchase by Eni and Shell of the OPL 245 offshore oilfield in Nigeria in 2011 from Malabu Oil and Gas, a company owned by former Nigerian oil minister Dan Etete.
Prosecutors alleged that just under $1.1 billion of the purchase price was siphoned off to politicians and middlemen, including Etete.
Prosecutors had called for Eni and Shell to be fined and for a number of past and present managers from both companies, including Descalzi, to be jailed.
The defendants all denied any wrongdoing.
“This judgment will continue to sting, as it is a real and visible defeat for global and Nigerian anti-corruption efforts,” he said.
Nigeria said it was disappointed with the outcome and would consider its position once it had read the written judgment.
“The Federal Republic of Nigeria will continue to hold those responsible for the OPL 245 fraud accountable, not only to ensure the people of Nigeria benefit from this valuable resource, but also to make clear its commitment to rooting out corruption in all of its forms,” said a spokesman for the Nigerian government based in London.
The defendants said the purchase price for OPL 245 was paid into a Nigerian government account and subsequent transfers were beyond their control.
The exploration licence for the field, some 150 km (95 miles) off the Niger Delta, has not been revoked but it has not been converted into a mining licence and no oil has been produced.
(Reporting by Emilio Parodi, Alfredo Faieta and Stephen Jewkes in Milan, Libby George in Lagos, Shadia Nasralla and Ron Bousso in London; Editing by David Clarke)