The 28-year-old Spaniard has agreed terms on a two-year deal with an option for a third year, while Lazio will receive an undisclosed fee.
"I'm delighted to have secured the services of Javi on a permanent basis," boss Chris Hughton said.
"He has played 34 games for us this season and the fact that we've signed him is a testament to the contribution he has made to the team since joining us last summer."
Garrido said: "I'm so happy to have signed full-time I am very comfortable with everything here - with the players, the technical staff and of course the fans.
"I am just very happy that we have managed to remain in the Premier League where we belong.
"Now I want to do everything I can to help Norwich continue to be successful in the Premier League. For me personally I am delighted to have secured my future playing in English football with Norwich."