The 33-year-old left Burnley at the end of June after the club declined to renew his contract and has signed a two-year deal with Jose Mourinho's side.
He joined the Clarets from City in 2018 for £3.5 million and made just three appearances for the side during the 2019-20 season. The last time he appeared in the Premier League was against Everton on Boxing Day 2018 when Burnley lost 5-1.
Hart joins the side as a backup to Tottenham manager Mourinho's first choice keeper Hugo Lloris. Tottenham are mindful of improving their homegrown quota to increase the overall squad available to Mourinho. Premier League rules dictate a maximum of 17 overseas players can be named in any 25-man squad and Mourinho only picked four homegrown players in February which restricted his squad size.
Sources have told ESPN that the club are also looking to extend Lloris' contract. The French international's deal expires in 2022.