Judge Motahar Hossain also fined Giasuddin Al Mamun, the business associate, 400 million taka (over $5 million) who has remained behind the bar since March 26, 2007.
Bangladesh's Anti-Corruption Commission (ACC) had accused Rahman and Mamun in 2009 of transferring 204.1 million taka (about $2.60 million) to Singapore between 2003 and 2007.
According to the case statement, Mamun extracted 204.1 million taka bribe from a local construction company and allegedly deposited the money in a Singapore bank, from where Rahman withdrew some money.
The chief prosecutor of the ACC, Anisul Haq, said he would appeal against the verdict.
In May, the court issued the warrant of arrest, saying it would ask the Interpol to help detain Rahman, also a senior vice chairman of Khaleda's Bangladesh Nationalist Party (BNP), as he has been living in London.
Rahman was arrested on March 7, 2007 on charges of corruption during the 2007-2008 military-backed caretaker government.
Khaleda Zia's son was arrested on March 7, 2007 on charges of corruption.
He went to London after he was released on bail in September 2008 for treatment reportedly on condition of not participating in any political activities during his stay there.
Khaleda, leader of the BNP, has said political row is to blame in both her sons' prosecutions during Prime Minister Sheikh Hasina 's incumbent government.
Earlier Khaleda's youngest son, Arafat Rahman, now reportedly in Thailand, was sentenced in absentia to six years on corruption and money laundering charges.
Since the end of her tenure in 2006, her eldest son Rahman faced 14 cases on charges of corruption, extortion and grenade attacks.