The 57-year-old German will begin the role on 1 January 2025.
"After almost 25 years on the sideline, I could not be more excited to get involved in a project like this," said Klopp.
"The role may have changed but my passion for football and the people who make the game what it is has not."
Energy drinks brand Red Bull owns RB Leipzig in Germany's Bundesliga, Austrian side Red Bull Salzburg and Major League Soccer side New York Red Bulls, as well as Brazilian side Red Bull Bragantino.
It also took a minority stake in Championship side Leeds and became the club's front-of-shirt sponsor earlier this year.
Red Bull says Klopp will not be involved in day-to-day operations but will advise teams on playing philosophy, transfer strategy and coaching development.
"Jurgen Klopp is one of the greatest and most influential figures in world soccer, with extraordinary skills and charisma," said Oliver Mintzlaff, the company's CEO of corporate projects and investments.
"In his role as head of soccer, he will be a game-changer for our involvement in international soccer and its continued development."
He began his managerial career at Mainz in 2001 before joining Borussia Dortmund in 2008, where he won two Bundesliga titles and reached the 2013 Champions League final.
He resigned in May 2015 to take a sabbatical but cut it short to succeed Brendan Rodgers at Anfield in October that year.
Red Bull has invested in ice hockey, extreme sports, motorsports and two teams in Formula 1, with Red Bull Racing currently holding both the drivers' and constructors' titles in the sport.
A news conference formally announcing Klopp's appointment will take place in mid-January.
