Earlier this week, Palace's first official offer for Benteke - worth £23 million plus a potential £7 million in add-ons - was firmly rejected, but the Eagles have improved with a sufficient enough offer to tempt the Reds into doing business.
The agreed deal consists of a £27 million up-front fee, with a further £5 million of potential additional instalments, and was accepted by Liverpool on Thursday.
The Belgian international will now be given permission to travel down to London and enter talks over personal terms and undergo a medical, with no hitches expected.
With Benteke left out of Liverpool's squad for their 4-3 win over Arsenal in their opening game of the new season on Sunday, having played no part in any of their pre-season games, a move away was inevitable.
Reds confident of recouping almost full fee they paid to sign Benteke just 12 months ago
Liverpool will at least recoup a sizeable sum of the fee they paid to make Benteke the second-most expensive ever signing in the club's history, with the add-ons in the deal deemed plausible.
Palace's first offer included an add-on which required Benteke to play 70 per-cent of Palace's games, scoring 20 goals and helping them to Champions League qualification for them to pay Liverpool £2.5 million - something Klopp and co. decided was too unrealistic.
But the renewed offer is more likely to see them earn back over £30 million for Benteke, who leaves having failed to make the impact he had hoped after sealing his 'big move' from Villa.
His absence hit Villa hard, with the relegated West Midlands club winning just three games in the 2015-16 and finishing 22 points off of safety.
However, despite directly winning 14 points, the 25-year-old was unable to command a regular role as the Reds' frontman with his playing style at odds to the demands of Klopp's defending from the front pressing style.
The striker's departure, believed to be on as much as £110,000-a-week at Anfield, is best for all parties involved with Benteke looking for more regular first-team football, Liverpool recouping a significant fee and Palace adding the quality they were in desperate need of up top.
With Connor Wickham and Fraizer Campbell their only striking options after the departures of Emmanuel Adebayor, Dwight Gayle and Marouane Chamakh over the course of the summer, Yannick Bolasie's £25 million move to Everton provided the funds for Palace to bring in Benteke.
It remains unlikely, however, that the money earned from the No.9's sale will be reinvested with Klopp having been keen toline his squad in recent months.