Tedesco has signed a contract that will last until the summer of 2023 and will take charge of Leipzig for the first time this weekend against Borussia Monchengladbach.
Earlier this week, Leipzig parted company with American manager Jesse Marsch following a run of three straight Bundesliga defeats, which left them 11th on the standings.
Assistant manager Achim Beierlorzer, who was placed in a caretaker role and oversaw Tuesday's 2-1 UEFA Champions League win over Manchester City has now left the club.
Tedesco was previously in charge of Schalke 04, whom he led to second position in the Bundesliga in the 2017/2018 season.
The 36-year-old's last managerial role was with Russian outfit Spartak Moscow from 2019 until this summer.
Tedesco will lead Leipzig into the Europa League after they finished third in their Champions League group behind Man City and Paris Saint Germain.
