Smith, who developed a reputation for playing exciting, attacking football while coaching Brentford, is a Villa fan and will replace Steve Bruce, who was sacked last week after the second tier side's dismal start to the season.
Former Chelsea and England skipper Terry decided to call time on his playing career last weekend and will re-join the Championship club as assistant coach.
He had been without a club since leaving Villa after their play-off defeat by Fulham at Wembley Stadium last season.
Villa have also appointed Jesus Garcia Pitarch as Sporting Director.
“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," Villa CEO Christian Purslow said.
“Dean has a clear and successful coaching philosophy as well as a real understanding of Aston Villa Football Club. He is also knowledgeable about the Championship...
“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."
Villa are 15th in the Championship with three wins in their opening 12 games.
