The tests confirm that original post-mortem blood samples were from driver Henri Paul and that he had three times the French legal limit of alcohol in his blood, the BBC said, quoting from a documentary it will screen Sunday.
Conspiracy theorists have claimed Paul was not drinking that night, contending the blood samples were swapped with blood from someone else who was drunk.
The BBC said a source with access to the French investigation reported that within the past year, French officials took a DNA profile from Paul's blood samples and matched it with his parents' DNA. It did not identify the source.
The driver, the 36-year-old princess and her friend Dodi Fayed, 42, died when their Mercedes crashed inside the Pont d'Alma tunnel Aug. 31, 1997, while being followed by media photographers.
Rumors and conspiracy theories continue to swirl around the death of the former wife of Prince Charles, heir to the British throne, despite a French judge's 1999 ruling that the crash was an accident. An investigation later concluded Paul had been drinking and was driving at a high speed.
An official British report into the crash, to be published Thursday, is expected to find her death was an accident, a London newspaper said late Saturday. The Observer said the report by former Metropolitan Police chief John Stevens also concludes that Paul was drunk at the time of the crash.
But other of Stevens' findings reported by the Observer were likely to fuel conspiracy theories.
The paper said Stevens would report that a U.S. secret service was bugging Diana's phone without the approval of its British counterpart on the night of her death. It said U.S. officials assured Stevens the secretly recorded conversations shed no new light on her death.
Stevens' report also will confirm claims that Paul was in the pay of the French intelligence services, the Observer said.
British police declined to comment on the BBC report or Stevens' investigation.
A former judge presiding over the British inquest into Diana's death said this past week that preliminary hearings would be held in public and not in private, as had been planned, after a protest from Fayed's father, Mohammed, who owns Harrods department store.
The inquest, convened and then swiftly adjourned in 2004, is due to formally resume next year. Preliminary hearings will be held Jan. 8-9 at the Royal Courts of Justice.