The former France head coach stepped back from his latest position with the federation (FFR) in December after being given a two-year suspended prison sentence and a €75,000 ($114,600) fine for corruption.
He denied wrongdoing and intends to appeal against his court punishments, which meant the FFR did not immediately oust Laporte and instead decided to render him effectively powerless pending the attempt to clear his name.
Sports minister Amelie Oudea-Castera called for Laporte to go in December, however, and he chose to permanently step down in the wake of clubs this week voting against his choice of president-delegate, Patrick Buisson.
Around 2,000 clubs took part in the vote, with 51.06 per cent saying they did not approve of Laporte proposing Buisson for the interim role.
The Rugby World Cup starts in France in September, and Laporte, president since 2016, had appeared eager to be back in charge of the FFR by then.
Les Bleus won the Grand Slam last year, and Laporte departs just eight days before the 2023 Six Nations begins.
Reports said Laporte delivered news of his resignation to the FFR executive committee on Friday morning local time at a meeting in Marcoussis, on the outskirts of Paris.
Oudea-Castera later said: "I can give you confirmation of the resignation of Bernard Laporte. I welcome this decision, it was necessary at the end of this consultation in which the clubs were massively mobilised.
"The ethics committee played its role of supervision in this time of consultation which went well with dignified debates. Bernard Laporte drew the conclusions, which is a good thing for French rugby, its values and the future."
Laporte stepped down from his role as vice-chairman of World Rugby within hours of his conviction in December, which also saw him banned from rugby involvement for two years pending the outcome of any appeal.
Laporte was released without charge this week after being detained as part of a tax fraud investigation.
His lawyer, Jean-Pierre Versini-Campinchi, said that Laporte had "neither been accused of having defrauded nor of having received any money".