Ali, 35, the son of Jordan's late King Hussein and Queen Alia, will become the youngest member of the ExCo after beating South Korean Chung, who has sat on the board since 1994, by 25 votes to 20 in a fight for Asia's vice-presidential seat on the committee.
Prince Ali, who has been head of the Jordanian FA since he was 25, becomes the third member of the Jordanian Royal family to occupy a seat on a major sporting governing body.
Before the vote was taken Prince Ali told Reuters: "I am optimistic, but in a secret ballot you never know. However, I think I can bring some new ideas to FIFA, it is an exciting time for Asian football and I am standing because I think it is time for a change."
The ensuing result strengthens FIFA president Sepp Blatter's grip on his position as he privately supported the prince against Chung, one of his perennial critics.
Blatter told reporters afterwards: "This is a surprise. After 16 years, probably the youth that wanted to come in has played the better card. However, I did not support anybody."
Chung has long been one of the most influential FIFA executive committee members and in the late 1990s was one of the architects of South Korea's bid to stage the World Cup in 2002.
Blatter himself was FIFA's secretary general before he beat UEFA president Lennart Johansson to become president in 1998.
In a separate vote between four candidates for two of Asia's other seats on the committee, Worawi Makudi of Thailand retained his seat and Vernon Manilal Fernando of Sri Lanka was voted on to the FIFA executive committee to replace Junji Ogura of Japan who was retiring.
