Terry had attracted interest from Premier League clubs including Bournemouth, Swansea City and West Bromwich Albion when it was confirmed he would leave Stamford Bridge after 22 years.
Chelsea announced in April that Terry would be leaving the club after last season, during which he made few appearances as Chelsea were crowned champions under Antonio Conte.
Reports suggest Terry will earn £60,000 a week with bonuses taking the total package to more than £4 million a year.
Terry told Villa's website: "It's a club I have admired from afar for many years".
"It wasn't a financial decision, if that was the case I certainly wouldn't be here", Terry added at his press conference.
He says he wants to help Villa get back into top flight football.
"My understanding of the situation is that John, with his relationship with Chelsea, was going to find it hard to be a direct competitor of them in the Premier League", Clement told talkSPORT.
Part of the agreement will see Unibet give supporters the chance to be amongst the very first to wear and play in the new Aston Villa kit in a tournament alongside Villa legends and celebrities at Villa's renowned Bodymoor Heath training ground.
"It's exclusively playing", he said. Terry would also be an extremely high-profile signing for Villa. "I think a lot of people have retired too early".
Villa did not offer the best financial deal but there is a massive mutual respect between the player, Villa's manager and the director of football.
"Playing against Chelsea just doesn't sit right with me, to be honest", he said following the confirmation of his Midlands move.
"It was bubbling once the season finished with phone calls, text messages, and I bumped into Steve in Portugal".
'It's a statement of intent to get someone of his calibre to come and be the big player we all know he is, ' said the Villa manager.