Bournemouth swoop for Palace striker Murray
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Murray agreed the contract with Eddie Howe's side after Palace accepted an offer of around £3 million for the 31-year-old.
"It feels great to finally be here," Murray told Bournemouth's website. "I've come across the club a lot in my career and it's been great to see it progress.
"The way the boys play football is very exciting. It's front-footed and it will be nice to try and get some goals from it."
After joining Palace on a free transfer in 2011, Murray scored 47 goals in 125 appearances and was a key figure in their promotion to the top flight in 2013.
A serious knee injury derailed his hopes of making an immediate impact in the Premier League and he was loaned to second-tier Reading last season before returning to Palace to score seven times in 15 appearances for Alan Pardew's men.
Pardew's pre-season signings of forwards Connor Wickham and Patrick Bamford meant there would be limited first-team opportunities for Murray this season and persuaded him to move to Dean Court.