The Australian joins the Premier League newcomers on a three-year deal, ending a 10-year association with Reading.
Federici is the second keeper to join Bournemouth in two days following the completion of a permanent deal for Artur Boruc, who spent last season on loan at the Goldsands.
He told the club’s website: “It was difficult to leave Reading because I had been there an extremely long time. I had a lot of success there and the fans were great for me, but I thought it was time I moved on.
“‘I’m looking forward to joining something special down here. It’s a team I admired last season, watching how they play their football.
“Having spoken to people like Ian Harte, who I’m close to, he couldn’t speak highly enough of the squad.
“As I said, I feel like I’m joining something special and I’m looking forward to working with the manager and the boys. I can’t wait to get started.”