Bielsa was sacked following the heavy defeat at home to Tottenham on Saturday, a result that leaves the team only two points above the relegation zone.
The West Yorkshire club have acted swiftly to name a successor, with Marsch agreeing to become their new head coach, pending international clearance, after putting pen to paper on a deal that runs to June 2025.
“We are delighted to welcome Jesse to the club and excited for him to lead us into this new chapter,” said Victor Orta, Leeds’ director of football, on the club’s website.
Orta added: “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.”
Leeds chief executive Angus Kinnear said: “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.”
Additional reporting from PA