The 40-year-old former England captain is leaving Dean Smith's backroom team in order to pursue his own managerial ambitions.
Terry does not have a job lined up but has decided to go now, with a year remaining on his contract, to avoid causing disruption during Villa's season.
Smith, who has reluctantly agreed to let Terry depart, is now seeking a replacement though no appointment is thought to be imminent.
Terry has been part of Villa's backroom staff since Smith was appointed boss in October 2018 and is a hugely popular figure with the club's players.
The former Chelsea defender had ended his own playing career at Villa Park, captaining the team during their failed promotion season under Steve Bruce in 2017-18.
In a statement, Terry revealed he had been mulling the "extremely difficult" decision to leave for several weeks.
He said: “It has been a tremendous honour and privilege to have spent these last three years at Aston Villa, but I feel now is the right time to make the extremely difficult decision to move on.
“I want to be as respectful to the manager and everyone at Aston Villa as I can and, having given my future serious consideration over the summer, I genuinely don’t feel it is fair to move into a new season without being certain of seeing that through.
“My immediate plan is to spend some quality time with my family and, thereafter, hopefully take up some invitations to visit clubs and mangers around Europe to develop my aim and objective of becoming a manager.
“It has always been my ambition to move into football management and, providing the right opportunity presents itself, I feel ready to take up such a challenge.
“I would like to thank Christian Purslow and our owners, Wes Edens and Nassef Sawiris, for believing in me and giving me the opportunity.
“And I will forever be indebted to the Gaffer for giving me the opportunity to start my coaching career at a such a wonderful club. I have loved every minute of it and learnt so much.
“I can’t thank Dean enough for the support and guidance he has provided me with and I’m sure he will continue to lead the club from strength to strength.
“Finally, I would also like to thank all the players and staff and wish them all the very best for the season ahead and say a huge thank you to the wonderful Aston Villa fans for their support.”