The 20-year-old made 58 first-team appearances for Liverpool after joining the club's academy from Wycombe Wanderers in 2011.
Neither club disclosed the transfer fee, but media reports said Bournemouth would pay a club-record 15 million pounds ($20.01 million) for the forward, who struggled to cement a place in Liverpool's starting lineup last season.
"He played plenty of football with Liverpool last season and we’re looking forward to seeing him continue to grow now with us, he’s a huge prospect," Bournemouth chief executive Neill Blake said in a statement on the club website (www.afcb.co.uk).
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Ibe had been tipped to fill the void left by Raheem Sterling departure to Manchester City last year.
His pace and direct running appealed to Liverpool manager Juergen Klopp when he took over in October and the winger enjoyed a run in the side before later finding himself on the fringes of the first-team squad.
Ibe scored just four goals in his time at Liverpool, although he ended the season with a fine individual effort against West Bromwich Albion.
(Reporting by Toby Davis; Editing by Ken Ferris)
