"We think that for the interests of Athletic it is best to have a change," club president Josu Urrutia told a news conference on Friday. "We haven't yet decided who will be his replacement."
The eccentric 57-year-old Bielsa, who has coached Argentina and Chile, took the Basque club on a roller-coaster ride for the last two seasons.
He guided them to the 2012 King's Cup and Europa League finals in his first year only to lose to Barcelona and Atletico Madrid respectively.
Bielsa was unable to repeat those achievements last season and had to settle for a 12th-place finish in La Liga.
Former Bilbao player Ernesto Valverde is favourite to replace him next season.
The 49-year-old Valverde, who left Valencia earlier this month, could return for a second spell at Bilbao where he coached for two seasons between 2003-05.