The Burkina Faso international made a superb start to life at the club by scoring a stunning goal in last night’s 3-0 Carabao Cup win at Bristol City.
Traore, who joined in a £19million deal from Lyon, played alongside Terry at Chelsea earlier in his career before moving to France in 2017.
Terry, who confirmed he had provided a character reference for the 25-year-old ahead of his move to Villa, is now backing him to shine in claret and blue.
“At a very young age at Chelsea he made an immediate impact,” he said. “He was unable to cement his place in what was a very experienced and able squad at the time.
“He went away from the Premier League but had the desire to come back and wants to prove himself at the very top. He has that opportunity now at Villa.
“Personally and professionally I am delighted to have him with us.”
Terry believes Traore’s trickery on the right flank will take attention away from Jack Grealish on the other, improving Villa’s attacking threat.
“He has the pace to get in behind and he has the quality, individually, to isolate people in one-on-one situations,” he said.
“I think we have that with Jack on the other side as well. Jack gets doubled up in a lot of games as well. To have him on the other side might free Jack up.
“He has the potential to beat players one on one and score great goals. Hopefully we can see more of that.
“It was important for him to get off to a good start. We saw Emiliano Martinez on Monday save a penalty (against Sheffield United) and then Bertrand come in and do that.
“He has not played for a while as well. To get the goal really topped it off for him.”
Traore’s strike was the highlight of an excellent performance at Ashton Gate from a much-changed Villa team.
Anwar El Ghazi and club record signing Ollie Watkins were also on target as Dean Smith’s men set up a fourth round tie at home to Stoke next week.
“It was important for players to come into the team, get minutes under their belt and show the manager what their worth is in the team and give him food for thought,” added Terry.
“We managed to bolster our squad over the summer and players are fighting for places, which is great.”
Smith remains keen to add another midfielder before next month’s transfer deadline and is interested in signing either Ross Barkley or Ruben Loftus-Cheek from Chelsea on loan.
Barkley, who joined the London club for £18million from Everton in 2018, has appeared as a substitute in both of their Premier League matches this season.
Loftus-Cheek, meanwhile, started the 3-1 opening day win over Brighton and it is unclear whether Chelsea would be willing to allow either player to leave during the current window.
Premier League rules mean Villa, who have already spent more than £75m, could only pursue a loan loan deal for one of them.
Smith is also hopeful of adding another forward to the ranks with Mbwana Samatta on course to complete a move to Fenerbahce.
The Tanzania international flew to Istanbul on Wednesday night and is poised to leave Villa after just nine months with the club.