The 31-year-old striker has joined the Cherries for an undisclosed fee, believed to be in the region of £5million.
Murray, who spent part of last season on loan with Reading, has signed a three-year deal with the south coast club.
"It feels great to finally be here," Murray told afcb.co.uk.
"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."
TRANSFER: @GM_83 has joined @afcbournemouth for an undisclosed fee. #CPFC We wish Glenn all the best at #AFCBpic.twitter.com/3bywV3WcpU
— Crystal Palace FC (@CPFC) September 1, 2015
BREAKING: #afcb sign @GM_83 from #cpfc on a three-year-deal: http://t.co/uqWoJShC8d#DeadlineDaypic.twitter.com/xIzTTKLMQ3
— AFC Bournemouth (@afcbournemouth) September 1, 2015