Opposition leader Jorge Segovia, president of first division club Union Espanola, took the vote 28-22 and will assume the ANFP chair in January 2011, an ANFP spokesman said.
Argentine Bielsa, appointed by Mayne-Nicholls in 2007, announced on Wednesday he would quit as coach if the opposition won the election. His last match in charge is expected to be a November 17 friendly against Uruguay in Santiago.
Shortly after steering Chile to the second round of the 2010 World Cup in South Africa, Bielsa had signed a new contract with Mayne-Nicholls, chairman of FIFA's inspection team that visited the countries bidding to host the 2018 and 2022 finals.
In a hastily arranged news conference, Bielsa listed a number of factors that he felt made him incompatible with Spanish businessman Segovia and said he would not stay on if Mayne-Nicholls lost the presidency.
Mayne-Nicholls told reporters at ANFP headquarters he would continue his work as a FIFA official and thanked Bielsa for his contribution to Chilean football and "through his message yesterday the legacy he leaves us for future generations".
Segovia, also at the ANFP, said: "I want to be president for all in Chilean football. This (outgoing) board leaves us with a very high bar to work towards and I want to take the opportunity to congratulate them on the job done."
INTERNATIONAL SUCCESS
Bielsa was in charge of a highly successful spell for the Chile team, steering them to the World Cup after a 12-year absence. They won two matches, their first victories at a finals in 48 years, before losing to Brazil in the second round.
The Argentine's popularity in Chile, with his attention to detail and professional approach to his job, good performances and results, transcended football.
He became a model for politicians and business people and was asked to give talks on his methods.
Segovia faces the task of finding a successor to Bielsa to take charge of Chile at next year's Copa America, the South American championship, in Argentina and the 2014 World Cup in Brazil.
The Spaniard had the support of a majority of Chile's 32 professional football clubs including the "Big Three", champions Colo Colo owned by Chilean President Sebastian Pinera, Universidad de Chile and Universidad Catolica.
The opposition criticised what they perceived as a very personal style of government by Mayne-Nicholls and his favouring the national team over the domestic game but his supporters have praised him for revitalising Chilean football.
