The Giants agreed to a five-year deal worth $11,150,000 with the safety from Miami, reports NFL Network's Adam Schefter.
Phillips was not immediately available for comment.
The Giants have big plans for Phillips, who was taken with the 31st and last pick of the first round.
New York lost starting free safety Gibril Wilson to Oakland in free agency. Veteran Sammy Knight was signed for the immediate future, but it still left the Giants with a future need, and Phillips more than fills it.
The 21-year-old started 33 of 34 games in three seasons with the Hurricanes, including all 12 this past season at free safety. He finished his career with 203 tackles, including 15 for losses. He also intercepted 16 passes, forced three fumbles and recovered one.
"There's a lot of things to like about Kenny Phillips," general manager Jerry Reese said on draft day. "We like his size and speed, he is multidimensional -- we like those kind of players. He played corner(back) before, and we think he can go down and play on a third receiver if he had to. He's smart and he's a good person."
Phillips plays a lot like Wilson. He has the ability to play close to the line and stuff the run and defend the pass. He also can play special teams.
Information from the Associated Press was included in this report