The 38-year-old, who helped Villa return to the Premier League last season, had 12 months left on his existing deal but will now remain at the club until 2021.
Terry had been mentioned as a potential successor to former Chelsea teammate Frank Lampard at Derby should he replace Maurizio Sarri at Stamford Bridge.
The new Villa contract for Terry now appears to have ruled out that possibility, leaving boss Dean Smith delighted the former Chelsea and England captain has decided to prolong his stay at Villa Park.
"I am really pleased that JT has extended his current deal as he is a pleasure to work with," Smith told the club website.
"We have had a successful start to our Villa coaching careers and JT has been instrumental in joining myself, Richard O'Kelly and Neil Cutler.
"He has complimented the team that we have and I have no doubts he will go on to be a top manager in the years to come.
'"Our focus now is on the coming season and to try to continue the progress we have had in the past eight months."
Terry enjoyed a glittering playing career, winning five Premier League titles, five FA Cups, three League Cups, the Champions League and Europa League with Chelsea.
He then spent his final season before retirement at Villa in 2017/18 as the club reached the Championship play-off final, losing to Fulham.
In October last year, Terry was appointed as part of Smith's coaching team following the latter's arrival as successor to Steve Bruce.
Terry played an important role as Villa again reached the Championship play-off final, clinching promotion to the Premier League with a 2-1 victory over Derby at Wembley last month.
Writing on his Instagram, Terry said: "I'm delighted to have extended my contract at Aston Villa.
"I've thoroughly enjoyed assisting, working and learning from the gaffer, Richard and Cutts, and look forward to doing so for the season ahead.
"Now tougher challenges are ahead as we focus on making our mark on the most competitive league in the world.
"I'm sure the fans will get behind us, as they always do, and help make Villa Park a tough place to come and play."
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