He lashed out at what he described as a "media lynching", saying the energy he had spent defending himself had hampered his work as minister.
An investigative website said he had spent large sums of taxpayers' money on gala dinners and refurbishing his apartment when speaker of parliament.
He denies any wrongdoing.
"The attacks and media lynching targeting my family force me to take the necessary step back... I presented my resignation to the prime minister this morning," said Mr de Rugy.
The Mediapart website accused him of hosting friends to luxury dinners, featuring lobster and vintage wines, while he was speaker of parliament, and spending public money to refurbish his government-provided apartment.
Mr de Rugy acknowledges hosting the meals, saying it was normal for the National Assembly's speaker, but has pointed out that he does not like lobster.
"I don't like it, I don't eat it, I have an intolerance for shellfish," he previously told BFMTV. "I don't like oysters... I hate caviar, and champagne gives me a headache."
The claims came in the context of the "yellow vests" protests over inequality, and accusations against French President Emmanuel Macron that he was a "president of the rich" because of his pro-business policies.
Mr de Rugy says he has had filed a legal complaint against the Mediapart website for defamation, accusing it of having a desire "to harm, smear and destroy".
President Macron said the move by the minister to resign was a "personal decision, which he respected, so [Mr de Rugy] could totally and freely defend himself," the Elysée presidential palace said.
Mr de Rugy's predecessor, TV presenter and environmental campaigner Nicolas Hulot, resigned last year, saying Mr Macron and his government had not given enough backing to his plans.