"He is very sick so he cannot perform all the political activities demanded by the role of senior joint general secretary. He needs long-term treatment to recover from his illness."
According to medical reports released last month, Rahman was injured when he was strung up a wall and dropped, fracturing two bones in his back.
The government has not commented on the torture allegations.
|Zia has said that corruption allegations
against her are politically motivated [AFP]
Rahman's departure from Bangladesh came hours after a reunion with his mother, who was released from prison on Thursday after spending a year there, also on corruption charges.
After visiting her son on Thursday, Zia said he would not return to politics until he was healthy.
"He will stay abroad and out of politics until he recovers completely," Zia told reporters.
"Doctors say it will take at least to three years to pull through."
Rahman was arrested on corruption charges in March 2007 and despite being granted bail faces 13 charges of corruption.
He has been accused of making millions of dollars for his own gain by influencing the awarding of state contracts during the BNP-led government's reign from 2001 to 2006.
His lawyers have denied the allegations against him.
Khaleda Zia, for her part, has claimed that the corruption charges imposed on her in September 2007 by Bangladesh’s military-backed interim government were an attempt to force her out of politics.
But the simultaneous release of Zia and Rahman is being seen by analysts as a move by the interim government to ensure that the BNP party stands in December elections and show that it is keen to restore democracy to the country.