The 24-year-old Torro Rosso driver won the race for the coveted drive ahead of former world champion Kimi Raikkonen, with talks between the Finn and Red Bull ending last month.
Red Bull team chief Christian Horner announced the Perth-born Ricciardo's arrival next season in a statement.
He said: "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 to choose Daniel."
Horner added: "He's got all the attributes that are required to drive for our team: he's got a great natural ability, he's a good personality and a great guy to work with.
"Daniel knows what the team expects from him; he'll learn quickly and it's very much a medium to long term view that we're taking in developing him."
Ricciardo has been sponsored by Red Bull since 2008 and he started driving for Toro Rosso last year, claiming 22 Formula One points from 42 Grand Prix races.
The Australian is following the path Vettel took in 2009 when he switched from Italy's Toro Rosso to their British-based sister team Red Bull Racing.
The new Red Bull man's best result was this season's seventh place in China.
Webber, 37, is leaving F1 to pursue a new career in sportscar racing with Porsche.
Vettel leads the 2013 drivers' championship on 197 points with Webber placed fifth on 115 and Ricciardo in 14th with 12 points.