Klopp, who ended a successful nine-year stint at Liverpool last season and has also coached Mainz and Borussia Dortmund in the Bundesliga, was named in his post last year but officially started this month.
"It's pretty much what I wanted to do. I finished seven months ago at Liverpool. I did that consciously," he told a press conference.
"A few months after that the opportunity came up. I don't want to be a passenger or a prominent person in the room. I really want to put some value on it."
Klopp joined Liverpool in October 2015 and won the Champions League, the Premier League, the Club World Cup, the FA Cup, the League Cup and the Super Cup, as well as the Community Shield during his time in charge. He had also led Dortmund to back-to-back Bundesliga titles in 2011 and 2012, a German Cup and a Champions League final in 2013.
He will not be involved in the day-to-day operations but act as an advisor for the Red Bull-owned clubs in Germany, United States, Brazil, Japan and Austria while also supporting the organisation’s global scouting operation.
He will also contribute to the training and development of coaches.
"I always wanted to try to learn new stuff and I felt immediately that it's exactly what I want to do. It's a different role."
Klopp said he no longer wanted to work as a coach, having done it for more than 20 years, and jumped at this challenge.
"I did not want to do that anymore. I wanted to get a new start and this is an opportunity. To add value," he said.
"How it will look we will see. There is not one plan that works for all teams. We want to be the best we can be. In each department, in each club."
Red Bull owns clubs on different continents and also has a stake in second division club Paris FC which Klopp visited days ago.
"I see myself as an advisor and a good advisor is part of the decision," Klopp said.
"I am the one with the most experience (within the organisation). It's a pretty young team so we are ready to go. Improve ourselves and by doing that improving the people around us."