The 31-year-old has signed a three-year contract.
“It feels great to finally be here,” Murray told Bournemouth’s official 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.”
Murray spent part of last season on loan with Reading, scoring eight goals in 18 league games.