They include a wife and children who disappeared from his Afghan camp at the time of the 9/11 attacks on the US.
The family's whereabouts have been a mystery for the past eight years, with reports that some of the children had been killed in bombings, while others had joined their father in planning terror attacks.
However, relatives said they found out last month that the group, including one of Osama's wives, six of his children and 11 of his grandchildren, had been kept in a high-security compound outside Tehran.
They have been prevented from contacting the outside world while Iran has repeatedly denied that any of the relatives were living in the country.
Members of the bin Laden family are now appealing for the group to be allowed to leave Iran and described them as the "forgotten victims of 9/11".
They told him how they had fled Afghanistan just before the September 11, 2001, attacks and walked to the Iranian border.
They were taken to a walled compound outside Tehran where guards said they were not allowed to leave "for their own safety".
The eldest of the children, Saad, was 20 at the time; Ossman was 17, Muhammad 15, Fatma 14, Hamza 12, Iman 9, and Bakr 7.
There had been speculation Muhammad was second in command of al-Qa'ida and that Saad instigated and plotted terrorist attacks until he was killed about 18 months ago by a US drone.
The relatives, however, said Muhammad was still living in the compound and Saad ran away less than a year ago in an attempt to find his mother.
A week after making contact with her brother, Iman escaped during a rare trip outside the compound and made her way to the Saudi Arabian embassy.
She is now living there while seeking permission to leave Iran.
Mr bin Laden said his relatives live as normal a life as possible, cooking meals, watching television and reading. They are allowed out only rarely for shopping trips.
Because several families are being held in the compound, some of the older siblings have been able to marry and have their own children.
"The Iranian government did not know what to do with this large group of people that nobody else wanted, so they just kept them safe; for that we owe them much gratitude, and thank Iran from the depth of our hearts," he said.
Mr bin Laden, who had lived with his father in exile in Sudan and Afghanistan but left before the 9/11 attacks, hopes the family will be given permission to leave Iran and join his mother, brother and two sisters in Syria or himself and his wife in Qatar.
He said: "They are all just innocent victims, just the same as anyone else hurt by the dreadful events of 9/11 and 7/7.
"These babies and children have never had any education, never hurt a single soul, never trained with any weapons or ever been part of al-Qa'ida.
"We just want to be together as a family. I have now got 11 nieces and nephews, born either in Afghanistan or Iran that I have never seen.
"Some may find this story unnerving, but the child can't be judged by the sins of their father."