The American has agreed a deal until June 2025.
Bielsa was sacked on Sunday after three-and-a-half highly successful years at the helm, with owner Andrea Radrizzani saying he “had to act in order to secure Premierliga status”.
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,” Victor Orta, Leeds‘ director of football, said on the club website.
Leeds are two points and two places above the drop zone but, with key players due to return from injury in the coming weeks, unhappy supporters wanted Bielsa, the man who restored their Premier League place after a 16-year exile, to see the job through.
Radrizzani saw things differently, wel, and made the change, with 48-year-old Marsch the man enlisted to lead a charge away from the bottom three.
A two-time winner of the Austrian Bundesliga with Red Bull Salzburg, Marsch last coached at RB Leipzig, whom he left after just 21 games in December.
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.”
Marsch said he was “honoured and excited” to take over at Elland Road.
He said in a video on the Leeds Twitter account: “The last phase of making this decision from everyone’s perspective came together pretty quickly, but it’s something I’m really excited about.
“I know what a big club Leeds is. I have ex-players that have played here, I’ve watched this club from afar for many years and I’m really honoured and excited to be here.”