The 24-year-old's Anfield career has been halted in the last two seasons due to injury problems.
In recent weeks, reports have emerged claiming that Kelly's representatives have been in talks with the London club over a £1.5m move.
It appears that Kelly's arrival at Selhurst Park is on the verge of being announced after Kelly wrote on Twitter: "I would like to thank all the managers at lfc for making my wish from the age of 7 come true playing for 1 of the biggest clubs in the world.
"most of all would like to thank the fans for supportin me since my home debut against Lyon oct 2009 even through injuries always by my side.
"Now to start a new chapter of my football career at crystal palace a great club with unbelievable fans excited already for the weekend."
Palace will begin the new Premier League season with a clash against Arsenal at the Emirates on Saturday.