The 36-year-old centre-back became a free agent on July 1 after ending his 22-year career with Chelsea.
Terry made 717 appearances for Chelsea and won 15 major trophies, including five Premier League titles.
He had a host of suitors in the Premier League as well as Villa's cross-city rivals Birmingham, with new boss Harry Redknapp telling talkSPORT he was keen on landing the former England captain.
But Terry opted for a move to Villa Park after meeting with manager Steve Bruce earlier this summer, having reportedly been offered the chance of moving into coaching at the club.