The goalkeeper, who is an England youth international, is a top talent that Arsenal were sad to see go to a Premier League rival.
Academy Manager Mark Harrison is looking forward to seeing the youngster develop at the club and is delighted to bring him in after many rivals wanted his services.
"We are delighted Owen has joined us," he said.
"As you can imagine, a player with his profile was highly sought after. He is a player we believe has high potential, having also represented England.
"He has very good athletic qualities and ball management skills, which really suit our style of play. We look forward to working with Owen and seeing how he develops over the next few years."
It has been reported that Villa will pay Arsenal £1m compensation for the teenager who made three appearances for Arsenal at Under-18s level last season.