Hart was dropped by City earlier this month after a string of high-profile blunders, but he is still first choice for England boss Roy Hodgson and played in the recent friendly defeat by Germany.
City boss Manuel Pellegrini recalled Hart for Wednesday's 4-2 Champions League win over Viktoria Plzen and the 26-year-old produced a string of saves as the hosts struggled at the back.
Richards is confident that Hart will put this difficult spell behind him and prove himself as one of the game's top keepers.
"In my opinion, he's one of the best in the world," said Richards.
"Obviously as a player you always go through difficult times but the best always rise to the top and he is top three in the world and definitely the best in England, that's for sure.
"I think he's mature enough, he's bright enough to get over this sort of hurdle.
"Everyone goes through a difficult spell in their career. He has gone through it and he's one of the best so he will get over it and I thought he did very well."
It remains to be seen if Pellegrini will restore Costel Pantilimon to the side for Sunday's Premier League clash with Swansea.
Richards admits the Romanian has seized his chance to shine in City's side.
"Pantilimon has come in and done really well, so it's a hard topic for me to really comment on," he said.
"All I can really say is both are quality players and I'm just glad Joe Hart is back to his best now and it's up to the manager to decide who he picks."