The 20-year-old winger joins on a four-year deal for an undisclosed fee, after the Reds beat Championship rivals to his signature.
Wilks excelled last season in League One with Doncaster Rovers, scoring 15 goals for the side that missed out in the play-off semi-finals.
He is the second player Barnsley have signed from Leeds this summer, after Aapo Halme, and the eighth new face in total.
A left winger, Wilks is likely to compete for a place with Mamadou Thiam who played every game in the promotion season.
Wilks is due to stand trial in May next year at Leeds Crown Court accused of violent disorder and assault occasioning actual bodily harm relating to an incident at the West Indian Carnival in Leeds in 2017.