It was such a massive move that it prompted coach Ben McAdoo to make a courtesy call to longtime starter Eli Manning.
McAdoo reached out immediately after the pick Friday night. He eventually touched base with Manning later in the evening.
The Giants said they didn't think they needed to discuss it with him before.
"We didn't have any conversation with Eli before we drafted, but we drafted a quarterback, and we are going to let our quarterback know that we are drafting a quarterback, of course," general manager Jerry Reese said Friday night.
Webb is the fourth quarterback selected since Manning came to the Giants during the 2004 NFL draft, not to mention the highest pick. Webb joins Ryan Nassib, Rhett Bomar and Andre Woodson.
Webb comes to a crowded quarterback room that already features Manning, recently signed Geno Smith, Josh Johnson and Keith Wenning.
Manning, 36, has three seasons remaining on his current contract, which will take him until he's 40 years old.
The hope is that Webb can sit and learn for two to three years before eventually taking over for Manning, a two-time Super Bowl winner.
"Couple years to be the caddie and learn the pro game and all the nuances of playing quarterback in this league," Reese said of his plan for Webb. "But he has all the tools. Hopefully he can sit on the sideline with a clipboard and learn the game."
The Giants think Webb has the best arm in the draft. That is why they were surprised to see him available in the third round. Even though they hadn't had much contact with him throughout the draft process, they thought the value was too good to let his talent go elsewhere.
The Giants had him graded "fairly high," according to McAdoo. They thought he would be selected long before they picked in the third round, and possibly even as early as the first. They were surprised to see him slip.
Reese and the Giants picked Webb despite not working him out prior to the draft. McAdoo had never even spoken to Webb before Friday night. His evaluation was based strictly off of film study.
Webb threw for 4,295 yards with 37 touchdowns and 12 interceptions last season at Cal. He began his collegiate career at Texas Tech, where he took the starting job from Baker Mayfield, who was a Heisman finalist this year at Oklahoma. Webb eventually lost Tech's starting job to Patrick Mahomes.
The Kansas City Chiefs selected Mahomes 10th overall in this year's draft.