Aston Villa statement: "The board of Aston Villa are delighted to confirm that Paul Lambert has been appointed Villa manager."
Lambert led Norwich to a 12th-place finish in the Premier League last month but angered the club this week when he offered his resignation following interest from Villa.
The Canaries refused to accept the Scot's resignation during the week but admitted on Friday their search for a new boss had begun, with Lambert wanting to leave.
It is believed Villa will have paid around £1million in compensation to ensure Lambert becomes their fourth manager in less than two years.