Keane will continue as Martin O'Neill's assistant with the Republic of Ireland national team while working at Villa Park.
"I look forward to getting to know the players, their strengths and weaknesses," he is quoted as saying by BBC Sport. "I've always had that pull to get back into a club.
"I had the situation with Ireland to consider but coming to work with Paul at Villa in the Premier League was too good to turn down."
The Villans start the new Premier League campaign away to Stoke City on August 16.