The FIA, the sport's ruling body, opened a tender to find a new promoter for the WRC in February after the previous promoter, North One Sport, had its contract terminated when its parent company CSI went into administration.
Red Bull Media House was one of three candidates that had been shortlisted by the FIA for the role. The other two were a South African partnership and Eurosport.
The WRC manufacturers, teams and stakeholders were told about the deal during Rally Finland earlier this month.
Citroen boss Yves Matton, whose team is sponsored by Red Bull, believes the move will be good for the sport.
"I think [Red Bull] Media House promoting the championship would be a good thing, but it would be different from Red Bull, which is the team sponsor," said Matton.
"When they do something, they do it properly and they don't just want to make a good name with the promotion. If they choose to invest in the World Rally Championship then it's because they want to make a proper job, otherwise they would not even attempt to do it."