The 61-year-old faces a tough ask in ousting incumbent Sepp Blatter as head of football's world governing body in the June election with the Swiss having held the position for 13 years.
Dr Chung, pictured sitting alongside Bin Hammam, famously questioned the Qatari's mental health two years ago at the Asian Football Confederation Congress, said he was the right man for the job.
"We welcome the candidacy of Asian Football Confederation president Mohammed Bin Hammam," Chung told reporters at a media conference in Seoul.
"Blatter has served as FIFA secretary general and president for 30 years. Now it's time for him to give way to a new person."
Chung, who surprisingly lost his FIFA vice-president seat to Prince Ali of Jordan at the AFC Congress in January, remains an influential figure in world soccer having been part of the FIFA executive committee since 1994 and his family owning the giant Hyundai conglomerate.
The Korean, honorary chairman of the Korean Football Association (KFA), was once considered a possible challenger to Blatter at the June 1 FIFA congress in Zurich and his presence in Bin Hammam's campaign could help sway votes.
Bin Hammam, who is touring the world canvassing support, launched his bid to become the first Asian president of FIFA two weeks ago in Kuala Lumpur when he revealed a manifesto based on making the organisation more open to the public.
Chung questioned Blatter's popularity.
"In terms of finances, FIFA is more successful than the (International Olympic Committee) IOC and the president should be admired, beloved and respected but Blatter is not.
"I can't say Bin Hammam is perfect but he is the right candidate to bring change and revolution to FIFA."
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