The Argentine takes over following the exit of Diego Alonso after Uruguay failed to reach the World Cup knockout stages.
"The fans are calling for games and emotions. The time has come," read a message on the team's official Twitter account, which also confirmed Bielsa's appointment.
Bielsa, who is expected to be presented at a press conference on Wednesday, returns to coaching following his departure from Leeds in February 2022.
Bielsa led Leeds into the Premier League after a 16-year absence.
The 67-year-old, who also had spells with Olympique de Marseille and Athletic Bilbao, has previously coached Argentina and Chile at the 2002 and 2010 World Cups respectively.
Bielsa's tenure will begin with two home friendlies against Nicaragua and Cuba next month.
