Tuanzebe spent the second half of last season on loan at Villa from Premier League rivals United and returned to the Villans in the summer transfer window.
The 20-year-old defender - who earns £260,000 per year as salary, according to Spotrac.com - will stay at Villa for the 2018-19 campaign and will be hoping to establish himself in the first team as the season progresses.
Chester joined Villa from West Bromwich Albion in the summer of 2016 for a transfer fee reported by The Daily Mail to be worth £9 million and has established himself as a key figure in the Villans’ team.
Tuanzebe told Villa’s official website about Chester: “Chezzie is solid, full-stop. First off, he has a fantastic character – he’s tremendous in the dressing room – incredibly lively.
“He’s a great skipper too – he’s good organisationally with the lads and he’s also a good person. He cares about the lads and wants to make sure everyone is alright.
“On the pitch, you can see those traits, too. He’s vocal, giving advice during the game, always talking to me. I like playing with him. He’s a top lad.”
Challenging for promotion
Villa reached the Championship playoff final last season, and Steve Bruce's side will be aiming to clinch promotion to the Premier League this campaign.
The Villans are 12th in the Championship table at the moment with nine points from six matches, two points behind sixth-placed Brentford.