The 24-year-old, who came through the Reds' youth system, has signed a three-year contract at Selhurst Park and could be in contention to play at Arsenal on Saturday.
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"I would like to thank all the managers at [Liverpool] for making my wish from the age of seven come true playing for one of the biggest clubs in the world," he wrote.
"Most of all [I] would like to thank the fans for supporting me since my home debut against Lyon in October 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."
Kelly made 33 Premier League appearances at Liverpool and also spent a spell on loan at Huddersfield Town in 2009.