The paintings, now worth at least 10.6m euros (£8.8m), were stolen from a London home in 1970 and bought in an auction by a Fiat worker.
Italian police unveiled the works in a press conference on Wednesday.
However, the Fiat worker now says he hopes "the judges will give us back the works of art".
"They were bought in good faith," he told La Repubblica.
"Above all, they were bought through the state, and the institutions can't deny this."
Identified only as "Mr Nicola", the former factory worker also described how he came to own the paintings, which were put up for auction after being found, abandoned, on a train.
"We'd just finished our night shift in the factory, and I was really tired," he said, "but I really wanted to go to the auction of the lost objects on the trains.
"I fell in love straight away with two pictures."
He said the paintings had originally been listed for 50,000 Italian lira (roughly £160 in 1970) but the price was reduced after "nobody stepped forward".
That triggered a bidding war between Mr Nicola and one other buyer, with the price increasing in increments of 500 lira.
"In the end I won with 45,000 lira," he said. "It wasn't a small sum for a migrant worker from Sicily. Including doing the night shift at Fiat, I used to get 200,000 lira a month.
"But I've always loved art. Instead of going to the cinema or the bar I prefer to put aside my money and go and look for curiosities and objects in the markets or the little auctions."
He hung the pictures in his living room in Turin and, after retiring to Sicily, in his kitchen.
"My son always asked many, many questions. He was fascinated by these pictures... he bought some books to try to do some research. Then one day he bought, at a second-hand bookstall, a biography of Bonnard."
While the son was flicking through the book he came across a photo of Bonnard sitting in a garden. "My son exclaimed, 'It's the garden in our picture!'," said Mr Nicola. "And in that way we began to understand."
They consulted experts and police were eventually alerted.
The Gauguin painting, titled Fruits sur une table ou nature au petit chien (Fruits on a table or still life with a small dog), had been painted in 1889 and was thought to be worth between 10m and 30m euros (£8.3m-£24.8m), police said.
The Bonnard, La femme aux deux fauteuils (Woman with two armchairs), is valued at 600,000 euros (£500,000).
For now, the paintings will remain in the custody of the paramilitary Carabinieri art theft squad, because the police have yet to receive an official notice that it is stolen.
The art squad said it had traced the paintings back to London, using newspaper articles from 1970 reporting the theft of a wealthy London family's collection.
Investigations are under way to establish who is the rightful owner of the painting.
The Italian police understand the works were the property of Terence Kennedy, an American author who married Mathilda Marks, of the Marks and Spencer empire.
However, both Kennedy and Marks are now dead and Mossa said they had been unable to establish an obvious heir.
Mr Nicola said he hoped the paintings could be returned and re-hung on his kitchen wall, but he accepts it is unlikely.
If he could keep one, he told La Repubblica, it would be the Bonnard. He also raised the possibility of donating the works to a museum.
"To my children I've always said, 'If you love art, art will re-pay you,'" he added.