According to Sport24, Ricciardo will be officially presented as Red Bull's new driver at the Belgian Grand Prix in Spa-Francorchamp next weekend.
The report further said that the 24-year-old Ricciardo has been a junior driver with Toro Rosso since 2008 and made his Grand Prix debut in Britain in 2011.
However, Red Bull motorsport chief Helmut Marko declined to confirm the development, saying that they will not make any announcement until the Belgian GP.
Webber will reportedly quit Formula One at the end of this year and drive in the LeMans 24 Hour race and sports car series from next year with team Porsche.
Webber has already raced at Le Mans twice but his campaign was overshadowed by a dramatic crash in 1999 that saw his Mercedes-Benz do a backflip at 270km/h.