The former Liverpool manager has been named new football director of Red Bull, which he will take up from January.
BILD says contrary to previous reports, Klopp's contract does not include a break clause.
And the German's deal will run for five years.
Klopp told the Red Bull website: "After almost 25 years on the sideline, I could not be more excited to get involved in a project like this.
"The role may have changed but my passion for football and the people who make the game what it is has not. By joining Red Bull at a global level, I want to develop, improve and support the incredible football talent that we have at our disposal.
"There are many ways that we can do this front using the elite knowledge and experience that Red Bull possesses to learning from other sports and other industries.
"Together we can discover what is possible. I see my role primarily as a mentor for the coaches and management of the Red Bull clubs but ultimately, I am one part of an organisation that is unique, innovative and forward looking. As I said, this could not excite me more."