Palmer Luckey, the founder of Facebook Inc.’s Oculus virtual-reality unit, confirmed Friday that he financially backed Nimble America, a pro-Donald Trump group that paid for advertising mocking Hillary Clinton.

Mr. Luckey, who in 2014 sold his company to Facebook for $2 billion, denied that he was a founder or employee of the group, which says on its website it supports “legal immigration” and “smart trade.”

“I...