According to the report, the country's Olympic Committee will "oversee participation of women athletes who can qualify".
Saudi officials say that with the Games now just a few weeks away, the only female competitor at Olympic standard is equestrian Dalma Rushdi Malhas.
Saudi officials added that there may be scope for others to compete and that if successful they would be dressed "to preserve their dignity", the BBC said.
In practice this is likely to mean modest, loose-fitting garments and "a sports hijab", a scarf covering the hair but not the face.
Malhas winning Bronze in Youth Olympics (Photo: EPA)
Malhas, originally a Palestinian, was born in the US, and trained in Europe for many years. In 2000, she was the first Saudi woman to compete in the Youth Olympic Games, winning a bronze medal in Individual Jumping.
The decision to allow women to compete in the Olympics is a dramatic development for the Saudis, who systematically exclude women from the public sphere.
The BBC reported that for the past six weeks there have been intense, behind-the-scenes discussions led by King Abdullah, who has long been pushing for women to play a more active role in Saudi society, leading to the historic decision.