The 37 year-old has penned a deal with the Cherries to the end of the season.
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Forster joins Bournemouth after coming off contract at Tottenham over the summer. He has remained without a club since the end of June.
"The opportunity arose and, for me, it was one that I couldn't say no to," he said.
"I am absolutely delighted. It's happened pretty quickly but I am delighted to be here and be a part of it.
"I am looking forward to helping the team and the squad, and contributing however I can for the rest of the season.
"You can really see the trajectory and the ambition of the club, and I think that was a very attractive thing for me."