Ricciardo was announced as Sebastian Vettel's 2014 Formula 1 team-mate on Monday night.
Red Bull created Toro Rosso out of the Minardi team for 2006 with the express intention of preparing drivers from its extensive junior programme for its senior squad.
Ricciardo, who has spent the last two seasons at Toro Rosso, becomes the second of its drivers to make the step up to Red Bull after three-time champion Vettel.
"When Dietrich Mateschitz acquired the team that became Toro Rosso, his stated aim was that it should be the final step in the training of young drivers, with the eventual goal of graduating to the 'senior' team," said Tost.
"Daniel's move thus vindicates the work of the Red Bull young driver programme and also proves that we at Toro Rosso have given him a good racing education."
Ricciardo's current team-mate Jean-Eric Vergne is expected to remain at Toro Rosso for next season. He was in contention for the Red Bull seat but was ruled out early on.
Tost added that there is "no hurry" to choose Ricciardo's replacement.
Raced for Toro Rosso from the start of 2006 until mid-'07 when he was sacked after falling out with the team. Retained Red Bull backing in America, rising to its NASCAR Sprint Cup team before being dropped at the end of 2010. Has four top 10 finishes in 118 Cup starts and currently a part-time start and parker and rallycrosser.
Briefly raced for Red Bull's a-team in 2005 before driving for Toro Rosso for two years. Was then dropped, but raced for Force India in 2009-10 and HRT in 2011. Now racing in Superstars tin-tops (pictured) and sportscars.
Raced for Toro Rosso from 2009-11 before being dropped. Still in the Red Bull fold as Red Bull's reserve driver but has little prospect of an F1 return next year. Racing for Toyota in the World Endurance Championship.
Pitched into F1 too early and with no testing in the middle of 2009 and was axed after two-and-a-half seasons during which neither he nor team-mate Buemi were able to assert themselves. Now on the sidelines and seemingly destined for IndyCar.
Set to remain at Toro Rosso for a third full season next year. His potential is highly-regarded by Red Bull, but he needs to add consistency to his game and deliver improved qualifying performances to stay in the Red Bull fold beyond 2014.
Neel Jani tested eight times for Toro Rosso in 2006. Subsequently raced in IndyCar with Red Bull support but now outside of the fold and competing in top-line sportscars. He will be part of Porsche's new LMP1 programme next year.
Brendon Hartley (pictured) appeared in the 2009 young driver test and has subsequently been a Mercedes simulator pilot and one-time tester alongside sportscar outings.
Mirko Bortolotti drove for STR in the same test and later fell out of single-seaters after winning Formula 2 in 2011. Now dominating the Megane Trophy.
Carlos Sainz Jr and Daniil Kvyat both tested for STR at Silverstone in July and are currently racing in GP3.