The sum eclipses the £10m the Cherries forked out for striker Benik Afobe in January.
The 20-year-old, who has penned a four-year deal with the south-coast club, has linked up with the squad at a pre-season training camp in Chicago.
Ibe scored four goals in 58 outings for the Merseysiders following his arrival from Wycombe in 2011.
The England U-21 international inked a new five-year contract with the Reds last May, but slipped out of favour under Jurgen Klopp.
