The 22 year old last played on 23 September last year in the 2-1 defeat by Manchester United, a game in which he suffered a serious knee injury that sidelined him for six months.
"I'm delighted to have signed. It means everything to me and my family. I've been at Liverpool since I was seven, so it's in my heart and I love the club," said Kelly.
"When you play in the Liverpool shirt, you have to show the fans what it means. I just love playing and trying my hardest for the supporters and for my family.
"Being a Liverpool supporter myself, it's brilliant to put the shirt on and I'm doing what I have loved doing since I was a kid. I'm over the moon.
"Today shows the faith that the club have in me and that the hard work I have put in since I was young has paid off. Hopefully I'll put the injuries behind me. We have excellent medical staff here, who are going to work me and keep me on top of my injury. I'll be coming back even stronger."