Hickey, the former head of the Olympic Council of Ireland and the European Olympic Committee, posted 1.5 million reais (£354,201) in bail, money loaned to him by an umbrella body that represents national Olympic committees.
"I shall grant the defendant Patrick his passport back as soon as he has signed the terms agreed," the judge in the case Marcelo Rubioli wrote.
Hickey was expected to sign immediately and leave Brazil, where he was arrested in August as part of an investigation into an illegal ticket-scalping ring during the Rio de Janeiro Olympics.
The 71-year old has maintained he is innocent of all charges.
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(Reporting by Rodrigo Viga Gaier; Writing by Andrew Downie; Editing by Ken Ferris)
