The deal for the 27-year-old former Manchester City left-back, subject to the usual rules of international clearance, sees Garrido arrive at Carrow Road looking to make the most of a second chance to shine in the Premier League.
Norwich confirmed the signing on their club website, and Garrido adds experience to a squad which survived comfortably in the Barclays Premier League last season.
Manager Chris Hughton said: "I'm absolutely delighted to be bringing in somebody of Javier's quality."
Hughton took over from Paul Lambert when he headed for Aston Villa after three hugely successful seasons at Carrow Road, which culminated in a 12th-placed finish last term.
The former Birmingham boss has been quick to tie up new deals for goalkeeper John Ruddy, who made his England debut against Italy in Berne last night, and striker Grant Holt, who handed in a transfer request at the end of last season.
Norwich have also brought in former Rangers defender Steven Whittaker, Jacob Butterfield, Michael Turner and Robert Snodgrass to bolster the squad for what is expected to be a testing Premier League campaign.
Hughton revealed those efforts will continue ahead of the transfer deadline and said: "We have a responsibility to make sure we have as competitive a squad as possible.
"Our endeavours are still there to strengthen the squad if we can, if it is right for the club, and that will continue through to the end of the month."
Celtic's Honduran left-back Emilio Izaguirre has also been linked with Norwich, but his price tag of £5 million could well be too high for the Canaries. Hughton, though, confirmed Norwich had been looking at possible back-up for Ruddy, with youngsters Jed Steer and Declan Rudd the other keepers.
"There are enquires which have been made, but it is just enquiries," said Hughton. "We have made them for numerous players and have a scouting network watching a lot of players."