The pair were found guilty of corruption in 2014 after a blockbuster trial over a cash-for-favours scandal.
In a written judgement, the Court of Final Appeal ruled that they had been "properly convicted of the offence of conspiracy to commit misconduct in public office".
Kwok had been on bail since July pending the appeal, but will now be back behind bars.
Former chief secretary Hui, 69, is the highest-ranking official in Hong Kong's history to be found guilty of taking bribes.
The seven-month trial centred on some HK$34 million ($4.3 million) in handouts, which the prosecution said were made to Hui by Kwok and his billionaire brother Raymond, to be their "eyes and ears" in government.
Hui was jailed for seven-and-a-half years in December 2014, while 65-year-old Kwok -- who was joint chairman of Hong Kong's biggest property company, Sun Hung Kai -- was sentenced to five years.
They lost an initial appeal bid in February last year before going to the Court of Final Appeal.
The case shocked the city and deepened anger over cosy ties between officialdom and big business.
Hui, Kwok, Kwan and Chan will serve out their sentences in the maximum security Stanley Prison.
Raymond Kwok was cleared of all charges during the 2014 trial.
The judgement said that Hui had been in "golden fetters" after he accepted a payment of HK$8.5 million shortly before he became deputy leader, when it was already known he would take up the position.
It added that the payment had been made to ensure an "ongoing inclination" on the part of Hui towards the Kwoks' company.
Hong Kong has been seen as relatively graft-free. But new cases in the semi-autonomous Chinese city have fuelled public suspicions over links between authorities and business leaders.
In a separate high-profile corruption case, former leader Donald Tsang, who ended his term in disgrace after accepting favours from tycoons, was jailed for 20 months in February after a trial found him guilty of misconduct while in office.
Hui was Tsang's chief secretary from 2005 to 2007.
Tsang, 72, was the highest-ranking Hong Kong official ever to be convicted in a criminal trial and jailed.
He was found guilty of failing to disclose his plans to lease a luxury flat from a major investor in a broadcaster, which was later granted a licence from the government while he was leader.
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