The game will be another milestone for Wembley, which hosted the National Football League's first International Series game in 2007.
Both universities boast devoted fanbases as college football, played by universities across the United States, is a key pathway to the NFL.
"We are proud to make history by bringing American College Football to London on a global stage," Brian Dubiski, Chairman and CEO of Union Jack Classic, said in a statement.
"Hosting two elite Big 12 programs at Wembley Stadium positions this matchup as the premier international showcase for our sport, and we look forward to delivering an unforgettable experience for fans and partners worldwide."