Faisal Hammash, Omar Sami Qaradhi and Motaz Al-Junadi are charged with sex offences in Antrim.
LOCOG said they had been told by the Jordanian National Paralympic Committee that they would not be entering the athletes into the games.
They said the athletes had returned to Jordan.
On Wednesday, a court in Coleraine, County Londonderry, heard that The King of Jordan has taken a personal interest in the case.
A Jordanian embassy official offered bail sureties at the hearing.
Bail of £500 ($793) was granted with a surety of £5,000 ($7,937) from the Jordanian government for each defendant.
The case had been adjourned while the judge considered the bail applications.
The squad is one of several international teams using the Antrim Forum sports complex as a training base in advance of the Games which begin in London next week.
The three men, two of whom compete in wheelchairs, are all members of the Jordanian Paralympics power-lifting team.
Faisal Hammash, 35, faces two counts of causing a child to engage in sexual activity.
Omar Sami Qaradhi, 31, is charged with three counts of sexual assault and one of voyeurism. At least two of the assaults were against children.
Motaz Al-Junadi, 45, faces one charge of sexual assault. All the offences took place between 16 and 20 August.
King Abdullah’s interest in the case was reported by one of his government officials who promised to return the accused men to Coleraine Court following the games if bail was granted.
The Jordanian Embassy in London released a statement saying it regretted the incidents that had led to the charges of the three members of the paralympic team.
“In line with its duties towards its citizens, the embassy provided direct consular support to the three members of the team charged with the offences,” it said.
“A senior diplomat from the embassy attended the hearings this morning at the Magistrates Court in Antrim, and posted bail for the three sportsmen pending their reappearance in Belfast for their trial in October.
“The embassy wishes to further express its appreciation to the courts for promptly appointing a defence lawyer for the three men and facilitating its Consular services to its citizens.
“The embassy in London wishes to reassure the courts of its continued cooperation and maintains utmost respect for the due process of the law.”
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