Leipzig have turned to their sister club from Austria, RB Salzburg, to swoop for Marsch, who will arrive at the Red Bull Arena at the end of this season, with Nagelsmann bound for Bayern Munich.
Marsch was previously an assistant manager at Leipzig during Ralph Rangnick’s spell in charge and he has also managed Major League Soccer side New York Red Bulls in the past.
Nagelsmann is excited that Leipzig have wasted little time in finding his replacement and has backed the former United States of America international to flourish in his new surroundings.
"I'm very happy that RB Leipzig have been able to quickly find a successor in Jesse Marsch," Nagelsmann said.
"It was important to me that the club find a good coach and that they wouldn't have to deal with too much uncertainty following the news of my departure.
"Jesse Marsch is a very emotional coach and has a good connection to his players. I will definitely look to speak with him at the end of the season. I wish him all the best here and that he continues the club's success."
Nagelsmann has the chance to end his two-year spell at Leipzig with a trophy as they play Werder Bremen in the semi-finals of the DFB-Pokal on Friday.
"There's nothing worse than losing a final. If we have the chance to win the trophy, then we'll do everything possible to make that happen,” Nagelsmann added on Leipzig’s official website.
"We don't need any extra motivation for Friday night. The cup is motivation enough. The team will give it everything they have to meet the expectations. They are highly motivated.
"I still have a good relationship with the team and spoke to the lads. All the outside noise won't affect them. All of my players want to continue improving.
"Our goal is to make it to [the final in] Berlin. We also want to break the 67-point mark in the Bundesliga, in order to set a new [club] record this season."
