The 23-year-old has agreed a four-year deal and will join for an initial fee thought to be around £25million.
Bailey's contract signing was broadcast live on his step-dad Craig Butler's YouTube channel in the early hours of Wednesday morning.
"Leon is a hugely exciting young striker with great pace and creativity,” said Villa boss Dean Smith.
“He has enjoyed a successful career at Leverkusen and we are now looking forward to watching him show his skills and talents for Aston Villa in the Premier League."
Bailey has joined Villa on the back of the best season of his career to date with his pace and versatility of particular appeal to Smith.
He becomes Villa’s third signing of the summer following the arrivals of Ashley Young and Emi Buendia, the latter in a club-record deal from Norwich.