The 19-year-old played seven times in Agar's final season at the KC Stadium in 2011 but failed to make a single appearance in Super League this season under his successor Peter Gentle.
The 6ft 3in Lyne, who made a try-scoring debut for Hull at the age of 17, has signed a three-year contract with the Wildcats.
Agar said: "He's a player with outstanding potential and possesses raw speed.
"He's a player for the future and I'm really pleased that we've been able to sign him. I'm confident that, given the chance to develop, he will become a top Super League player."
Lyne added: "Rich gave me my first opportunity as a young kid and I'm looking forward to working with him again."
- Super League