The Aussie defender has signed a four-year deal worth an initial fee of around £3m fee which could rise to £6m including add-ons and bonuses.
"I'm really looking forward to the opportunity here," he told the club's official site.
"It all happened quite quickly. I knew there was a bit of interest and then they put the bid in, Liverpool accepted and we went from there really.
"Bournemouth did really well last season and I think the club can be a great team in the Premier League for many years to come. They're just getting started really.
"I think it'll be a good fit for me and I can't wait to get going here."