The Liga side has decided against renewing the Argentine's stay in the Basque region and could now name Ernesto Valverde as his successor in the coming days
The 57-year-old initially took charge of the Basques two years ago and led the club to both the finals of the Europa League and Copa del Rey in his maiden campaign, along with a sixth-placed finish in La Liga.
However, he was unable to repeat his successes of 2011-12 last term, having presided over a relegation battle for much of the season, and his contract will now not be renewed as a result.
"The board unanimously decided against renewing Marcelo Bielsa's contract because we believe that a change is in the best interests of Athletic," said president Josu Urrutia in a statement.
Urrutia also hinted that Ernesto Valverde - recently unemployed following his stint at Valencia - could return to Athletic as coach for a second spell after revealing that the club are keen on appointing a former player.
"From tomorrow we will begin looking for alternatives. We want an ex-Athletic player [at the helm] if possible. We will look for the profile of a person that is integrated into the club as soon as possible," he concluded.