The 22-year-old made his debut against Bradford Bulls in March and has gone on to make six more appearances, scoring his first try against Catalan Dragons on Sunday.
Green told www.hullfc.com: "It has been a pretty good week to score my first try and then to sign a new deal, so I'm really pleased."
He went on: "I am thankful to Peter Gentle for my opportunity this season and hopefully a new contract is the reward for my efforts this year and a chance for me to progress.
"Hull FC is my home-town club and there is no other place I want to be playing. I've enjoyed my spells on loan at York and Doncaster, but there is nothing like playing in the Black and White at the KC Stadium, it's very special.
"Hopefully I'll get to enjoy that a lot more now and my focus is on my development and performances every week to make sure I retain my place in the team for the rest of the season."
Head coach Gentle has been forced to throw a number of his young players into action this season because of injury problems, and he praised Green's contribution.
"It's rewarding when you can put your faith in the young guys in the squad and know that they will make a telling contribution, whether it is their first or 50th game," said Gentle.
"The pleasing aspect about Chris has been his attitude and patience, he has worked hard on his game throughout the season and, when a chance finally came to play, he grasped it with both hands."