The 48-year-old comes in as a replacement for Marcelo Bielsa, who was sacked on Sunday after three-and-a-half-years in charge, with Leeds hovering just around the relegation zone in the Premier League.
Marsch was recently in charge of RB Leipzig, where he was sacked in December after just five months in charge, and has also previously coached RB Salzburg and New York Red Bulls.
Speaking about the appointment, Leeds United Director of Football Victor Orta said: "We are delighted to welcome Jesse to the club and excited for him to lead us into this new chapter.
"Jesse is someone we identified a number of years ago during his time at Red Bull Salzburg and we believe his philosophy and style of football aligns with that of the club and will suit the players very well.
"We have a long-term plan and firmly believe he can take Leeds United to the next level and are excited for what the future holds."
Chief Executive Angus Kinnear added: "We are really pleased to have quickly secured the services of our first-choice head coach.
"Whilst the short-term objective for Jesse is obvious, we believe he has the courage and ambition to build on the strong foundations we have created over the last four years and elevate the performance of the club over the long-term.
"He had a great deal of success with New York Red Bulls and Red Bull Salzburg and has demonstrated during our many meetings that he is a great fit with the footballing culture of Leeds United.
"At this challenging time, it is important that the club remains united from top to bottom. The fans have been amazing throughout Andrea's tenure and we have no doubt they will unite behind Jesse and ensure the team quickly returns to winning with style."
Marsch’s first game in charge of Leeds will be against Leicester City on Saturday.
