"Welcome JT to Birmingham city...Aston [email protected] Announcement shortly!," Tony Xia posted on Twitter in a sideways dig at the club's cross-city rivals, Birmingham City, who had also sought to sign the 36-year-old centre-half.
Terry became a free agent at the weekend after 22 years at Stamford Bridge where he played his entire career in the Premier League.
The Birmingham Mail and other papers reported Terry had signed a one-year deal and already flown to Villa's pre-season training camp in the Algarve to meet his new teammates.
He made his final appearance for the champions in May, leaving to a guard of honour 26 minutes into the game to correspond with his shirt number.
But, despite interest from West Bromwich Albion, Stoke City and Bournemouth, he has been persuaded to drop down to England's second tier by Villa manager Steve Bruce.
Villa are former European Cup holders who were relegated from the Premier League in 2016. Despite spending heavily under Chinese owner Xia, they failed to gain instant promotion and finished a disappointing 13th last season.
Enter a name and e-mail address and we will e-mail this website link too them.