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.
Teixeira could be called in for questioning.
"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.
ISL went bankrupt in 2001.
The BBC, which said 175 secret payments were made by ISL between 1989 and 1999, also named Confederation of African Football (CAF) chief Issa Hayatou and South American (CONMEBOL) head Nicolas Leoz of Paraguay.
They and Teixeira are members of FIFA's Executive Committee.
The MPF has asked the police to investigate whether any part of that money entered Brazil illegally through companies in tax havens belonging to Teixeira.
Teixeira has denied any wrongdoing.
