Terms of the contract were not disclosed by the team.
Myers played last season for the Oakland Raiders, and visited the Giants' New York facility on Saturday. Apparently the Giants liked what they saw enough to make an offer right away.
"I'm definitely excited. When you join an organization like the Giants it's a great opportunity and I'm excited to be here and to get started," Myers said, according to the team's website.
The Giants lost Martellus Bennett, their starting tight end last season, to the Chicago Bears at the start of free agency. Myers, 27, is a 6-foot-4, 250-pound player who caught 79 passes for 806 yards last season in Oakland.
"The opportunity to play in New York, to play on a big stage and to win ballgames, that's what you strive for as a player -- to be in contention to make the playoffs," Myers said, according to the team's website. "I had a pretty good feeling this was going to work out. I'm excited and I'm ready to get to work."
The Giants have had a busy Saturday after a measured start to the free agent signing period. The team also signed former Dallas Cowboys linebacker Dan Connor and, according to a source, also added former Raiders wide receiver Louis Murphy.