Glennon replaces Colt McCoy, who is currently a free agent. The Giants had spoken to McCoy about a potential return after he filled in admirably during a pair of starts, including a stunning upset of the Seattle Seahawks.
Glennon, 31, spent last season in Jacksonville. He started five games and threw for 1,072 yards with seven touchdown passes and five interceptions.
Glennon has appeared in 34 career games over eight professional seasons. He has thrown for 6,235 yards with 43 touchdowns and 25 interceptions, but his teams have won just six of his 27 starts.
His role in New York will be as Jones' backup and sounding board. The Giants have been adamant about being fully committed to Jones.
"We've had Daniel for two years; we've done the evaluation on him and we really believe he's the guy. No reason to go look [for a starter]," general manager Dave Gettleman said earlier this month. "What we're doing isn't fantasy football, we're not playing, we're not doing that. We've got a conviction on him, he's everything we want, he's got all the physical skills and again I say this all the time, the kid just finished his second year of NFL football. How many of us after two years at our new job were great? No, we all start at point A and we hopefully get to point Z, but the one common denominator is it takes time. Everybody has to understand that. We believe in Daniel, and that's where it is."