Klopp revealed on Wednesday that he would be leaving Dortmund at the end of the season, saying he no longer felt he was the right man to take them forward.
Tuchel, who took charge of Mainz a year after Klopp left the club to join Dortmund in 2008, has been out of work for a season having taken a break from the game.
He remains under contract with Mainz until the end of June, from which moment he will become the new head coach of Dortmund.
A Dortmund statement read: “The eight-time German champions Borussia Dortmund have appointed Thomas Tuchel as their new coach from July 1, 2015. The 41-year-old will receive a three-year contract.”