The 2015 MLS Coach of the Year will take over for Marco Rose, who departs at the end of the season for Borussia Monchengladbach
And Marsch, who has worked under Ralf Rangnick this season as an assistant at RB Leipzig, has been named his successor, effective at the end of the current campaign.
“I am really pleased and feel honoured to be able to work for this fantastic club as their next coach,” Marsch said in a statement. “I will give everything to further continue the extremely successful work here.
“That is going to be a new challenge for me, and I can’t wait for it.”
Salzburg sporting director Christoph Freund also released a statement saying: “Jesse Marsch is a coach who allows us to determinedly continue the path we have taken.
“We have followed his career and development very closely in recent years, and we have spoken often.
“We are completely convinced of him both as a professional and as a person. He knows our philosophy and way of playing football very well.
But it was with New York, where he took over in 2015, that the former U.S. international bolstered his reputation, as his squad was perpetually near the top of the Eastern Conference.
Marsch led New York to the league’s best record in 2015, capturing the Supporters’ Shield, and won MLS’ Coach of the Year award that same season.
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He inherits a team that is accustomed to domestic success, having won the last five Austrian Bundesliga crowns and look on pace to take a sixth this season.
He will be looking bring more success in Europe however, as the club has not managed to make the Champions League group stages during their consecutive title run, falling at the playoff round this season.