The Belgian striker is currently on his way to London for a medical and contract talks, with the transfer fee set to hit £32m through add-ons.
Alan Pardew’s side had already seen an offer rejected by the Reds, who were not impressed by the number of clauses on offer.
Reports also claimed the deal was set to be hijacked by Premier League rivals West Brom, forcing Palace to turn to Chelsea outcast Loic Remy instead.
But Palace have finally won the race for Benteke’s signature, and Pardew will be hoping his new forward is fit in time to face Tottenham at White Hart Lane on Saturday.
Jurgen Klopp is sure to be pleased by the deal, having recouped almost all of the £32.5m fee Liverpool paid for Benteke last summer.
The former Aston Villa star scored just 10 times in his single Anfield season, and his style of play was not suited to Klopp’s high-intensity game.
Benteke will now be looking to rebuild his reputation at Selhurst Park, while Liverpool could spend some of their new money on Porto ace Bruno Martins Indi.