Terry, 37, joined Villa on a one-year deal last summer after leaving Chelsea and was appointed captain. The last of the ex-England defender’s 36 appearances came in Saturday’s play-off final loss to Fulham.
“I will look back on my time here and think about how close we were to reaching our goal,” said Terry.
The ex-England captain said Villa manager Steve Bruce had been “instrumental” in him joining and had taught him things that will “stay with me forever”.