The 42-year-old will continue in his role as No.2 to Republic of Ireland manager Martin O'Neill - a position he has occupied since November last year.
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"I am delighted to be joining Aston Villa and I look forward to what promises to be an exciting challenge," Keane said.
"I am grateful to both Villa and the Football Association of Ireland for making this happen and I would like also to thank Martin O'Neill.
"I am relishing the prospect of linking up with Paul Lambert and combining both roles to the full advantage of both Villa and Ireland."
Lambert added: "Roy has a great knowledge of football, on the coaching side as well, and he'll be a great asset and a big help to everybody here at Aston Villa.
"I'm really looking forward to working with him and I'm delighted that he's here.
"As a player, he was one of the most accomplished in the history of the Premier League and he's brought that experience gained over many years into his career in coaching and management. The players will love working with him.
Goalkeeper Shay Given and youth-team coach Gordon Cowans were promoted following Culverhouse's sacking, but it remains to be seen what their roles will consist of following Keane's hiring.