The club has been searching for a replacement for Paul Heckingbottom since sacking him on June 1 after less than four months in charge at Elland Road.
Bielsa has signed a two-year deal, with the club holding an option for a further year.
The Argentinian has managed Chile as well as his home nation and has worked at a number of high-profile European clubs, including Athletic Bilbao, Marseille and Lazio.
“I am delighted to accept the role of head coach at Leeds United,” Bielsa said.
“It has always been my ambition to work in England and I have had several opportunities to do so during my career, however I have always felt it was important to wait for the right project to come along and so when a club with Leeds United’s history made me an offer, it was impossible to turn down.
“I am excited for the challenge ahead and I look forward to collaborating with Victor, Andrea and Angus, as we work hard to achieve great things at this football club.”
Bielsa was available after being dismissed as by French Ligue 1 side Lille in December, following a run of just three wins in 13 games.
The 62-year-old’s appointment means Leeds will start the season with a new boss for a fifth successive year.
The pedigree Bielsa brings will raise hopes of a return to the Premier League for the first time since the Yorkshire club were relegated in 2003-04.
“I am thrilled to welcome Marcelo and his staff to Leeds United,” Leeds chairman Andrea Radrizzani said.
“He is a coach that I have admired for many years and when the opportunity arose to bring him to Elland Road, we made it our top priority for the summer.
“Marcelo has a wealth of experience and he will use that to create a new culture and a winning mentality at our football club.”