The 20-year-old forward has agreed terms with the South Coast club after the Reds accepted a £15 million bid from the Cherries last week.
Negotiations between the two Premier League clubs saw buy-back and sell-on clauses inserted into the deal, with Liverpool opting to protect themselves in case Ibe excels under Eddie Howe.
Several other clubs were said to be interested, including Rafael Benitez's Newcastle United and West Bromwich Albion, but after mulling over whether to wait and see if he received any other bids, Ibe chose to make the move to the Vitality Stadium.
An official announcement is expected to follow by the end of the week, with the England Under-21s international then likely to fly to the United States to join Bournemouth's pre-season tour of Chicago and Minnesota.
Ibe's unsurprising exit follows frustrating campaign
Ibe had a below-par season in 2015-16, despite scoring his first goal for the club in November and netting his first Premier League strike with a stunning solo goal on the final day of the season.
Having been tipped to fill the shoes of countryman Raheem Sterling, who left for Manchester City 12 months ago after a controversial saga, Ibe's inconsistent form failed to command a regular starting berth under Jürgen Klopp.
Viewed as one of the club's brightest young talents, Ibe's departure completes a tumultuous 18 months for the player. He only signed a new five-year contract last May, following an impressive first-team breakthrough that came after he was recalled from a loan spell at Derby County in January.
However, Liverpool could not turn down the opportunity to earn such a huge windfall for a player whose last season was so disappointing, even though he is still just 20.
With Sadio Mane recruited to bring extra depth in attacking positions, in addition to Adam Lallana, Philippe Coutinho, Roberto Firmino and even Lazar Markovic and Sheyi Ojo, Ibe's opportunities were likely to be limited this coming season and £15 million was too good to turn down for a squad player.
Ibe, who made 58 senior appearances at Anfield since joining from Wycombe Wanderers' Academy back in 2011, will instead look to realise his potential at Bournemouth as they try to build on their maiden top-flight season last term, when they finished 16th.
There, he will replace Matt Ritchie who recently left for Newcastle in a £12 million switch, and will more than likely be a regular fixture under his highly-rated compatriot Howe.
While it would be no surprise if Ibe, privately, viewed the move as a backwards step - regular game time at this time in his development could help to determine whether he can become a regular at Premier League level over the coming years or not.
Canos and Skrtel on the verge of sealing respective deals
Of Liverpool's other imminent departures, the Independent are reporting that Sergi Canos is close to sealing a £2.5 million move to Norwich City.
He signed a four-year deal with the Canaries on Tuesday to end the race for his signature, with Bristol City and Brentford among the other clubs competing to bring the Spanish winger in.
Canos, who rejected Liverpool's contract offer having entered the final year of his existing deal, could yet return to Merseyside with a buy-back clause - as well as a sell-on fee - been included in the deal.
The deal could eventually rise to £4.5 million, with add-ons - thought to be based around appearances and achievements - also incorporated.
Martin Skrtel is also close to ending his eight-and-a-half year spell with Liverpool. He arrived in Istanbul on Tuesday, ahead of a £5.5 million transfer to Fenerbahce, and could put pen-to-paper to sign for the Turkish giants on Wednesday.
The 31-year-old's departure has been a long time coming and Klopp saw no place for him in his squad after Joel Matip's arrival on a free transfer.
Speaking to journalists shortly after landing at the airport in the Turkish capital, Skrtel insisted that Fenerbahce is "a giant club" which is why he "accepted the offer."
"I came here today to make the last call," the defender, who signed for Liverpool from Zenit St Petersburg back in 2008. "Hopefully tomorrow we can complete everything and I can be pictured as a Fenerbahce player. But there is one last step and then we'll do that interview."