Marie Madeleine Mborantsuo, the president of the court, says Ali Bongo received nearly 41.8 percent of the votes.
Second- and third-placed candidates Pierre Mamboundou and Andre Mba Obame are among those who filed complaints on Sept. 19. The two accused Bongo of "serious manipulation" and called for a re-count.
The court had one month to return a verdict. The inauguration date can be set now that the court ruled on Monday night.
Bongo was the African country's defense minister and eldest son of longtime ruler Omar Bongo, who ruled the country for more than 41 years until his death in June.