Garrett signed for the veteran's minimum, $650,000.
The money to ink Garrett became available when starting QB Kerry Collins signed a two-year extension on Wednesday, extending his contract through the 2004 season.
The Giants expect Garrett, who will be entering his 10th season, to compete with Jesse Palmer for the backup role.
Collins received a signing bonus of $5.85 million. Salary breakdown will be available shortly. Collins previous contract would give him a cap number of $8.78 million .
The move saves the Giants about $1.4 million.
To make room for Garrett, the Giants also cut quarterback Phil Stambaugh.