Leipzig parted ways with Marsch after a 2-1 defeat at Union Berlin on Matchday 14, with Achim Beierlorzer stepping in to oversee an impressive 2-1 win over Manchester City in the UEFA Champions League on Tuesday.
Interim coach Beierlorzer has now made way for 36-year-old Tedesco, who is making his return to the Bundesliga after spending the best part of two years in Russia with Spartak Moscow.
Born in Italy and raised in Germany, Tedesco enjoyed a brilliant start to his coaching career. He took his first senior role with second-tier Erzgebirge Aue in March 2017 and inspired a remarkable turnaround to save them from relegation.
He was still just 31 when he switched to Schalke ahead of the 2017/18 season, guiding them to a runners-up finish in the Bundesliga in his first year.
A poor run of form resulted in the Royal Blues changing direction in March 2019, but Tedesco bounced back in Russia. He joined Spartak in October 2019 and led them to second - their best placing in four years - in 2020/21.
Tedesco - who graduated from the DFB coaching school with the best marks in a class that included current Bayern Munich supremo Julian Nagelsmann - left Russia in the summer after deciding not to extend his contract.
The former VfB Stuttgart U17 and Hoffenheim U19 coach takes over a side that have dropped to 11th in the Bundesliga after losing their last three league matches. Leipzig next face Borussia Mönchengladbach at home in a Matchday 15 fixture this Saturday.