Ricciardo is replacing fellow Australian driver Webber and linking up with three-time world champion Sebastian Vettel.
Webber, who has had a tense relationship with Vettel, is quitting F1 at the end of the season to race sports cars for German manufacturer Porsche.
Red Bull says the 24-year-old Ricciardo has signed a multi-year agreement.
“I feel very, very good at the moment and obviously there’s a lot of excitement running through me,” Ricciardo said. “Since joining F1 in 2011, I hoped this would happen and over time the belief in me has grown. Next year I’ll be with a Championship-winning team, arguably the best team, and will be expected to deliver. I’m ready for that. I’m not here to run around in 10th place, I want to get the best results for myself and the team.”
Ricciardo was initially the front-runner to replace Webber, and the decision was expected to be made at last weekend’s Belgian Grand Prix, but it was put delayed due to speculation that 2007 F1 champ Kimi Raikkonen would leave Lotus to join Red Bull next year.
“It’s fantastic to confirm Daniel as the team’s race driver for 2014. He’s a very talented youngster, he’s committed, he’s got a great attitude and in the end it was a very logical choice for us,” Red Bull team principal Christian Horner said. “He joined the Red Bull Junior Team in 2008 and we’ve seen in his junior career in Formula 3 and Renault World Series that he’s capable of winning races and championships. He’s stood out in each of these categories and we’ve followed his progress with great interest.”
Two-time former champion Fernando Alonso, who is having a difficult campaign with Ferrari, was also linked to Red Bull. But the Spanish driver recently gave his public backing to Ferrari.