The police and the federal prosecutor's office (MPF) made the announcement on Tuesday following media allegations against Teixeira, president of the Brazilian Football Confederation (CBF) and the local 2014 World Cup organising committee.
"The investigation into Teixeira will open this week. It will be conducted by the anti-financial crimes bureau," a police spokeswoman told Reuters by telephone.
"Federal prosecutor Marcelo Freire asked head office of the Federal Police in Rio de Janeiro to open a police investigation of the president of the CBF for the crimes of illegal transfer of money to Brazil and money laundering," the MPF said.
The investigation will centre on accusations by the BBC of three top officials of football's world governing body FIFA, including Teixeira, of taking bribes over the appointment of International Sports and Leisure (ISL) as its marketing arm.
They and Teixeira are members of FIFA's Executive Committee.
