The 47-year-old lifelong Villa fan has been named Steve Bruce's successor after the club agreed a compensation package with Championship rivals Brentford to secure his services.
Smith was on the five-man shortlist drawn up by Christian Purslow, the club's chief executive, becoming established as a front-runner after Thierry Henry and Rui Faria dropped out of the race.
Talks with former Walsall boss Smith progressed quickly on Wednesday once Villa had reached an agreement with the Bees.
Terry, who also interviewed for the managerial post last week, joins as his assistant, returning to the club five months after his exit as a player. Villa have also confirmed the appointment of Jesus Garcia Pitarch as their new sporting director.
Smith is a lifelong Villa fan and is known for his attractive style of play - having guided the Bees into promotion contention this season.
He now departs Griffin Park for B6, with his first game due a week on Saturday, when Villa host Swansea looking to turn around their current win-less run.
Smith was always viewed as a contender to replace Bruce after the latter was dismissed last week.
Villa also held an interest in Celtic boss Brendan Rodgers but it was Smith who gradually came to the fore during an extensive, thorough process.
Purslow described the appointments of Smith, Terry and Patrich as a "new era" for the club.
"We are delighted to secure their services after an extensive search." he 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."
“The board welcomes him to the club and is looking forward to working with him and his staff.
“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 U23s and into the first-team.”