The judge overturned a lower 2013 acquittal by a lower court of Tarique Rahman, who lives in exile in London and now faces a ban from politics.
He was also fined 200 million taka ($2.5 million), the attorney general said.
The 51-year-old is the eldest son of opposition leader and two-times former prime minister Khaleda Zia and was considered her political heir apparent.
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"The high court said Tarique Rahman influenced political power to help his close friend Giasuddin Mamun to get and then launder 200 million taka," deputy attorney general Moniruzzaman Kabir told AFP.
The move comes at a volatile time in Bangladesh, which is reeling from a wave of deadly attacks by extremists.
Earlier this month five armed men stormed an upscale cafe in Dhaka's diplomatic zone and killed at least 20 hostages including 18 foreigners, in an attack claimed by the Islamic State group.
Police say a local militant group the Jamayetul Mujahideen Bangladesh (JMB) was behind the attack.
A week later, suspected militants from the same group attacked the nation's largest Eid prayer congregation, killing three people, according to police.
The Bangladeshi government says those attacks and a number of other killings of foreigners and religious minorities are part of a plot to destabilise the country.
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It has blamed the main opposition Bangladesh Nationalist Party (BNP) and its militant ally.
There was no immediate comment from Zia's party on her son's conviction, but an aide to the opposition leader said the case was politically motivated.
"There is no evidence which shows that Tarique Rahman took or laundered any money," Shimul Biswas told AFP.
"The aim is to keep him (Rahman) away from politics and to prolong one-party rule in the country."
The BNP, founded by Rahman's father and popular army strongman Ziaur Rahman in the late 1970s, has been in disarray recent years.
It boycotted the last general elections in 2014, allowing Zia's bitter rival Sheikh Hasina's party to win without even contesting most of the parliamentary seats.
Last year Prime Minister Hasina's secular government launched a crackdown in which thousands of BNP activists were detained and prosecuted for violent protests that left nearly 150 people dead.
Meanwhile the judge who acquitted Rahman in 2013 has since fled the country and is now believed to be in Malaysia.
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Prosecutors said Rahman would now face a ban from politics unless the Supreme Court overturned his conviction.
Legal experts said Rahman, who also faces several more charges of graft, would have to surrender to the court before he could appeal.
Nonetheless his lawyer Mahbub Uddin said they would appeal the verdict.
"We hope we'll get justice," he told reporters.
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