Carlo Ancelotti has asked to be released from his contract at Paris St Germain, according to sporting director Leonardo.
Bayer Leverkusen forward Andre Schurrle remains hopeful of leaving the Bundesliga club in the summer.
The 22-year-old, who is a product of the Liverpool academy, has made seven appearances this season.
His last game came 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."
The day after fellow defender Jamie Carragher announced his retirement at the end of the season, Brendan Rodgers was pleased to see another local lad commit his future to the club.
Rodgers said: "Martin has shown a commitment to our vision here. He is a young player who really impressed me when I came in.
"He was exceptionally good in the games he played earlier in the season."
The club's managing director Ian Ayre said: "It's fantastic news and it runs on from various other players who have committed to us.
"I think everybody has been starting to see and enjoy Martin's potential and the work he has showed to get into the first team and these are the things we are looking for.
"He was very unfortunate to get his injury but he has worked very hard with the physios and the medical team and hopefully we'll see him back soon.
"Signing him up for the long term is very important for us."
Kelly joins the likes of Luis Suarez, Martin Skrtel, Daniel Agger, Jonjo Shelvey and Raheem Sterling in agreeing a new deal at Anfield since the arrival of manager Brendan Rodgers.