"Lleyton has surprised me," said 20-year-old Belgian Clijsters, who became the first Belgian to be ranked the game's top player in August this year.
"He invited me for dinner on a boat and suddenly unveiled a ring and earrings. I didn't know what hit me, but I'm very happy about it.
"In Australia, being engaged means a lot," added Clijsters, who won nine WTA Tour titles this year. "But there are no concrete plans (for a wedding date). But I'm extremely happy with my early Christmas present."
Australian Hewitt, the men's world number 17, won the U.S. Open in 2001 and last year's Wimbledon crown.