Wiggins, an 18-year-old forward who played high school basketball at Huntington Prep School in West Virginia, had narrowed his choices to Kansas, Florida State, Kentucky and North Carolina.
"This was a pleasant surprise because we never had an idea which way he was leading," Kansas Coach Bill Self said in a statement Tuesday. "Andrew did this the exact way he said he was going to. He played his cards very close to his vest as did his mother and father.
"He's a tremendous talent and a terrific kid. Probably an even better kid than he is a talent. We think he has a chance to be about as good a prospect as we've ever had."
Wiggins is 6-foot-8 and was selected the Naismith Prep Player of the Year for 2013. He averaged 23.4 points, 11.2 rebounds, 2.6 blocks and 2.5 assists in helping Huntington Prep to a 30-3 record last season.
Wiggins is the son of former NBA player Mitchell Wiggins.