Garrido made 49 appearances for Manchester City between 2007 and 2010.
"Ever since my first day here my main thing was to join permanently," he said.
"They have shown confidence in me. I have played so many games and have been comfortable with everyone.
"After the last game against West Brom I was so happy because I knew I would be here permanently. It was a good moment for me. It is always tough to go to Manchester and get a good result. But we don't have any pressure.
"I admit I was a little bit worried (about relegation). In the Premier League it is difficult to get points.
"Everyone was a little bit worried, but in the end the team showed their character and the result on Saturday was amazing.
"You had to see the dressing room to see how happy everyone was. The job was done. But now we need to finish well and next season everyone has to improve.
"I am the kind of player who always wants to improve. Next season will be exciting."