The 25-year-old has agreed a long-term contract at Villa Park for an undisclosed fee, thought to be worth in the region of £19million (€20.5m).
“I’m excited to be back (in England),” he told Villa TV. “I always wanted to come back to the Premier League.
“I had to follow my own way as well and gain some more experience. I think it is the right time to come back.
“I think I’m coming back as a better player, with more experience. And this is the right place for me to come back. It’s good.”
Traore cited the presence of John Terry, with whom he shared a dressing room at Stamford Bridge, as a factor in the transfer, while he also mentioning Zimbabwe’s Marvelous Nakamba and Anwar El Ghazi as former team-mates from his time in the Eredivisie.
"I played with JT at Chelsea, I spoke to him," he continued.
“I spoke to the manager, spoke with the sporting director as well and some players I used to play with – Nakamba and El Ghazi.
“I spoke to Nakamba, I talked to him a little bit about the club. Many things made me take the decision to come here. I'm happy."
Although the move is subject to international clearance, manager Smith is pleased to have the forward in his ranks.
"We're delighted that Bertrand has chosen to come to Villa," he told the club's official website.
"He's a player with immense talent who will really enhance our attacking options."
Traore made his senior international debut for the Stallions at the age of 15 years in a friendly match against Equatorial Guinea.
He has also represented the West African country at three Africa Cup of Nations tournaments.
Aston Villa begin their 2020-21 Premier League campaign on Monday evening against Chris Wilder’s Sheffield United.