The 31-year-old scored 47 goals in 125 appearances for Palace, including 31 in his successful 2012/13 term where he played a crucial role in the club's promotion to the Barclays Premier League.
"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."
Murray spent part of last season on loan with Reading, where he scored eight goals in 18 league games before returning to Selhurst Park after Christmas.
Murray first made his mark at Carlisle and Rochdale before joining Brighton & Hove Albion in January 2008. He then moved to Crystal Palace on a free transfer in 2011.
The 6ft 2 striker was selected in the Football Manager Team of the Decade at the Football League Awards earlier this year, as managed by Eddie Howe.