Smith – a lifelong Villa supporter – joins from Championship rival Brentford and replaces Steve Bruce, who was dismissed on 4 October after a run of one win in nine games left them in the bottom half of the table.
Terry, who announced his retirement from playing on Sunday, spent last season with Villa, who have also announced Jesus Garcia Pitarch as their new sporting director.
Pitarch has previously been director of football at Valencia and Atletico Madrid in his native Spain.
Villa's CEO Christian Purslow said: "These three appointments represent the start of a new era and direction at Aston Villa and we are delighted to secure their services after an extensive search.
"Dean has a clear and successful coaching philosophy as well as a real understanding of Aston Villa. He is also knowledgeable about the Championship.
On Terry's return, he added: "John is one of the most decorated players in English football, has an affinity with the club and is ready to make the next step in his career working alongside Dean.
"And Jesus also brings a huge amount of experience in his particular role having worked with some of the biggest clubs in Europe. He will ensure the club has an integrated approach running from the academy through the Under-23s and into the first-team."
Belgium assistant coach Thierry Henry and long-time Jose Mourinho assistant Rui Faria had both been linked with the vacant post since Bruce's departure.