The 20-year-old was released by Manchester United at the end of the 2007/2008 season and instead of turning professional, he joined Hoddle's academy in Spain and becomes the first player from there to sign a permanent contract with a club.
Hoddle told Lincoln's official website: "To see Chris sign for a progressive Football League club is a fantastic feeling and all of the coaching team here can feel very proud of themselves.
"He is a player who we feel has a bright future in the game and the fact that he was on Manchester United's books shows that he's got something about him. He's a natural striker and his main asset is his movement off the ball.
"A lot of big name players such as Ian Wright and Alan Shearer were released by clubs at an early age so it just goes to show that with hard work, dedication and commitment that a second chance will come along. The name of Chris Fagan is certainly one to watch out for."