Bielsa set to become new Bilbao boss
The 43-year-old former player and team captain defeated incumbent Fernando Garcia Macua, scooping 53.36 percent of the votes cast by club members, the Basque side said on their website.
Urrutia campaigned with a commitment from Bielsa, who coached Chile at the World Cup finals in South Africa last year, and the Argentine will be appointed to replace Joaquin Caparros.
Caparros had coached the side for the four years of Garcia Macua's presidency and his contract expired at the end of June.
Bilbao are one of only four clubs in La Liga, along with Barcelona, Real Madrid and Osasuna, who are owned by the club members (socios), and who get to elect their president every four years.
They have around 35,000 socios and said there had been a record turnout at the polls.
Bilbao are famous for only fielding players of Basque origin and along with Real and Barca are the only clubs never to have been relegated from Spain's top division.
Under Caparros, they finished sixth in La Liga last May and qualified for next season's Europa League.