Defender Richards, 26, made 179 league appearances for City since 2005, but moved away from Eastlands on transfer deadline day after failing to impress manager Manuel Pellegrini.
The 13-time England international also saw his past two seasons derailed by injury - experiencing a six-month layoff due to a knee problem in 2012-13 and two hamstring issues last season.
Richards also said he turned down a loan offer from a rival Premier League club, as he chased a new challenge in Italy.
"Manchester City offered me a four, five year contract to stay because I've been there so long and I was in their plans, but for me, I wanted to come somewhere where I could sort of be given a fresh start and hopefully I can become the number one here as well," he said.
"It's been 12 years with Manchester City and over the last year or 18 months I've not played as much as I've wanted to.
"I had interest from other English teams but when I spoke to the people at Fiorentina, they made me feel very welcome, they told me what they wanted to do here, and I thought with my ability and my attributes, that I could help them achieve what they want to do."
Richards said the writing was on the wall for him in Manchester, with Argentine Pablo Zabaleta keeping him out of the right-back role.
"Obviously for any player when you're not playing it's frustrating but, you know, Zabaleta was having a really good season," he said.
"Sometimes as a professional you've got to understand that. And in my eyes it looks like it was - he was - number one choice. When [Roberto] Mancini was there he would rotate the full backs and when we won the league, I actually played more than Zabaleta and, obviously, had a really good season.
"But as I was coming back from injury, Zabaleta was playing really well, so the manager didn't really want to change. And he was doing well so I decided it was time for me to leave."
