The Spanish left-back penned a five-year contract with the Serie A side after passing a medical this morning, sealing his departure from Manchester City.
Kolarov moved the other way last month, six days before City confirmed they had agreed a fee with Lazio for the sale of Garrido.
The 25-year-old is now eager to relaunch his career after making just 49 Premier League appearances in three seasons.
"Replacing (Kolarov) is an important responsibility," said Garrido. "Now I'm here and he is at Manchester, it's a new stage in my career, with new team-mates.
"I really hope to give everything I have inside to be able to reach an important aim, whether on a personal or group level.
"I am really happy to be here, this club is one that is respected in Italy and it is very well known and appreciated on a European level too," he added.
"For me it is a new experience which gives me so many positive emotions. I hope to do really well."
Garrido moved to Eastlands for £1.5 million from Real Sociedad in the summer of 2007 and played the majority of their matches during his first season before falling down the pecking order after the arrival of Wayne Bridge.