The Scottish manager had an offer of resignation rejected by Norwich City but the two clubs have now reached an agreement over compensation for the 42-year-old
A statement on Villa's official websitesaid: "The board of Aston Villa are delighted to confirm that Paul Lambert has been appointed Villa manager."
Lambert tendered his resignation this week in an attempt to push through a move to Villa, who have been looking for a manager since Alex McLeish was relieved of his duties last month.
Norwich prohibited Lambert from talking to Villa earlier this week and therefore refused his resignation.
It appears, though, that a compromise has been reached which will see the Scottish boss move from East Anglia to the Midlands and take charge of a side that finished perilously close to the relegation zone, in 16th place, last season.
Norwich are believed to be discussing a compensation package for Lambert's services but it is understood that the £1m figure quoted is being dismissed by Villa officials, who believe that the sum is void due to a clause in his contract that allowed him to speak to another Premier League club.
Lambert was instrumental in Norwich's rise from League One to the Premier League in two seasons and then guided the Canaries to a 12th-placed finish in their first year back in the top flight.