The Eagles will pay a potential further £5million dependent on certain criteria being met during the 25-year-old's stay at Selhurst Park.
Benteke is scheduled to travel to London for a medical on Friday.
The deal should mean Liverpool recoup most of the £32.5million they spent on the striker last summer in bringing him to Anfield from Aston Villa.
Palace's failed in their initial bid earlier in the week of £23million plus £7million of add-ons, but this latest offer reduces Liverpool's losses on the player.
Benteke scored 10 goals in 42 matches for Liverpool but it was his lack of suitability for Klopp's methods, rather than his overall ability, which was his downfall at Anfield.
Source: PA