"It's absolutely clear that there was technological fraud. There was a concealed motor. I don't think there are any secrets about that," Cookson told a news conference.
The man elected to fight the long-standing scourge of doping in his sport also insisted there would be "no place to hide" for anyone attempting to cheat with motorised help.
Yet the 19-year-old Van den Driessche denied suggestions she had deliberately cheated in the women's under-23 race and was in tears as she told Belgian TV channel Sporza: "The bike was not mine. I would never cheat."
Van den Driessche said the bike looked identical to her own but belonged to her friend and that a team mechanic had given it her by mistake before the race.
The bike was taken for inspection along with others after she had pulled out on the last lap of Saturday's race with a 'mechanical problem' and had to walk to the finish.
"It wasn't my bike, it was my friend's and was identical to mine," Van den Driessche told Belgian TV channel Sporza.
"This friend went around the course Saturday before dropping off the bike in the truck. A mechanic, thinking it was my bike, cleaned it and prepared it for my race."
Van den Driessche said she feared her career could now be over but she still hoped for a second chance and was not afraid of any investigations into the case.
"I'm aware I have a big problem. I have done nothing wrong," she said.
In a sport that has long battled doping problems, suggestions and rumours of 'motorised doping' have floated around too but nothing has been uncovered in major competitions until this case.
UCI regulations on 'technological doping' were introduced last year with guilty riders liable to a minimum suspension of six months and a fine of between 20,000 and 200,000 Swiss Francs.
The governing body had brought in bike checks for road racing over the past season, including at the Tour de France where winner Chris Froome's bike was among those tested, a move that Froome applauded because "of all the rumours that are out there."
The Van den Driessche case prompted Cookson, who confirmed the case would be investigated by the UCI's disciplinary commission, to pledge riders would be protected against technological fraud.
"We've heard some stories for a long time now about the possibility of this," he said.
"I am committed and the UCI is committed to protecting the riders who do not want to cheat in whatever form and to make sure that the right riders win the race.
"To all the people who want to cheat, yesterday we sent a clear message: we will catch you and we will punish you because our technology to detect such fraud seems to work."
The UCI reportedly used a computer which can read radio frequencies to detect the hidden motor and then removed the seat post to see wires sticking out.
"There is no place to hide," Cookson added.
The affair quickly caused a furore at the cyclo-cross championships with Belgian national coach Rudy De Bie talking of his "disgust" and telling Sporza: "My relationship with her (Van den Driessche) is over."
Great Britain team manager Chris Young, who had celebrated a win in the race by Briton Evie Richards, told Cycling Weekly: "Every rider just can't believe what has happened. It's as bad as drug doping if not worse.
"It's not just a girl who has allowed it to happen. Someone has put the motor in. It makes you wonder who else has them."
