Financial details were not disclosed, but British media reported that Villa would pay about 8 million pounds for the 33-year-old, who made 22 appearances for Burnley in all competitions last season. The deal takes Villa's summer spending past £120m as they prepare for a first season back in the Premier League.
Aston Villa have completed the signing of goalkeeper Tom Heaton from Burnley.
"Quite simply a situation arose this summer, where he is in the final year of his contract, there was contact from Aston Villa and I believe he has been offered a very good contract for him and his family".
Having commenced his career at Manchester United, Heaton joined Cardiff in 2010 and later had a spell with Bristol City prior to joining Burnley in 2013.
Zimbabwe global midfielder Marvelous Nakamba was unveiled as an Aston Villa player on Thursday, becoming the fourth Zimbabwean to play in the English Premier League.
The goalkeeper said there was "momentum" at Aston Villa after their promotion from the Championship in May.
'He's done fantastically well for Burnley over the past few years and his experience and knowledge of the Premier League will be a major asset to us this season'.
Smith had this to say on his 12th summer recruit: "Marvelous fits the criteria of the type of player we were looking for".
The second announcement was the signing of Zimbabwean midfielder Marvelous Nakamba from Belgian side Club Brugge.