The season-ending event was plagued throughout by rain and heavy winds, which made the famed Valderrama golf course unplayable two straight days, and caused the second and third rounds to be suspended.
Sunday, there was some rain during an early start, but the final round was played under mostly sunny skies.
Kjeldsen finished at 8-under 276, winning the championship by two strokes over Germany's Martin Kaymer (68) and England's Anthony Wall (69).
"Winning is not easy," the Dane said. "There's a lot of good players out here."
Despite ending in a tie for 32nd, Sweden's Robert Karlsson captured the tour's Order of Merit title.
"It's fantastic," Karlsson said after learning he was the tour's earnings leader for the first time, and will take home the Harry Vardon Trophy.
This season, he won twice, finished second twice and third four times.