The 22-year-old was one of six players arrested and bailed as part of a probe by the National Crime Agency, which was acting on information passed to them by a Sunday newspaper.
The Latics responded by suspending Montano without pay on Sunday, 8 December and have now terminated his contract.
Oldham director Barry Owen insisted they had made the right judgment in deciding to axe Montano.
"It's hit a lot of people in the football world and certainly our fans," he said. "It's been a very, very difficult week and the investigation itself had to be conducted and that's the conclusion we've reached.
"We wouldn't be making the decision if we weren't confident."
Montano has been bailed until April but Oldham are adamant that the decision to sack him will not prejudice the legal proceedings.
A statement on the League One club's website, issued through CM Solicitors, said: "After a thorough investigation carried out by Oldham Athletic Football Club relating to the conduct of Cristian Montano and following lengthy discussions with our team of legal advisers at CM Solicitors, a decision has been made by the club board to dismiss the player forthwith.
"Notwithstanding and without prejudice to the ongoing criminal investigation, it is our view that the player's conduct, in not only bringing the name of Oldham Athletic but also the football authorities into disrepute, amounts to very serious breaches of club discipline, and therefore constitutes gross misconduct.
"Oldham Athletic take matters such as this extremely seriously and believe it was essential to act as swiftly as possible in conjunction with our legal advisers to investigate and deal with this matter decisively once they became aware of the allegations and irrespective of any other investigations and proceedings by other agencies."
Born in Colombia, Montano moved to London as a child. He joined West Ham as a trainee and signed as a professional in August 2010 but did not make any first-team appearances.
After loan spells at Notts County (twice), Swindon, Dagenham and Redbridge, and Oxford, he signed for Oldham in August 2012.