Teixeira said he was stepping down from FIFA's executive committee for personal reasons. He had been a member of the committee since 1994 and until recently was seen as a possible successor to FIFA president Sepp Blatter.
The resignation came in a letter to Nicolas Leoz, the head of the South American Football Confederation (Conmebol).
Conmebol did not give any details but said Teixeira's decision was "irrevocable".
His departure means FIFA has lost four members of its 24-person executive committee to corruption scandals in the last two years.
Teixeira's resignation brings down the curtain on a long and controversial career.
He took over as head of the Brazilian Football Confederation in 1989 and while Brazil won the World Cup twice during his time in office, the period was also notable for the constant allegations of corruption and shady business dealings.
A Congressional inquiry in 2001 accused him of 13 crimes ranging from tax evasion to money laundering and misleading lawmakers, although no charges were brought.
Last year, the former head of the Football Association David Triesman said Teixeira offered to back England's bid to host the 2018 World Cup in return for favours.
In February, the Folha de Sao Paulo newspaper said a company linked to Teixeira had overcharged the organisers of a November 2008 friendly match between Brazil and Portugal.
Teixeira denied wrongdoing in all cases but the allegations came at the same time as c riticism of Brazil's World Cup preparations were mounting.
Tensions boiled over this month when FIFA's interlocutor for the World Cup Jerome Valcke criticised the slow pace of progress, saying "things are not working in Brazil" and that Brazilian organisers needed "a kick up the backside."
His comments caused a storm of protest and Blatter was forced to apologise to Brazil's President Dilma Rousseff.
FIFA is worried Brazil is not building stadiums, hotels and particularly airports quickly enough or on a grand enough scale to cope with the 600,000 fans who are expected to arrive for the tournament.