Villa’s options narrowed in the wake of Thierry Henry and Rui Faria ruling themselves out of a move, paving the way for Smith to take over at the club he grew up supporting.
Smith has received plenty of praise for introducing an attractive style of football at Brentford since he took charge in 2015.
It is understood compensation is around the £300,000 mark has been paid with Smith now tasked with replacing Steve Bruce.
Terry had also been in the running for the job after calling time on his playing career this week.
The Chelsea legend spent the final season of his career at Villa last season, guiding them to the play-off final before suffering defeat to Fulham.
But Terry has now opted to take his first steps into coaching as Smith’s assistant, after the latter walked away from Brentford.
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 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.”
Smith’s first game in charge will be at Villa Park when they welcome Swansea on Saturday, October 20.
Villa sit 15th in the table with 15 points from their opening 12 matches.
The Championship club are without a win in their last four matches.