Gakpo, who has made 106 appearances for PSV in four years after graduating from their academy system, was part of the Dutch side that were knocked out of the World Cup by eventual champions Argentina in the quarter-finals.
The deal between the Dutch side, who currently sit third in the Eredivisie, and Liverpool has not been officially announced but club general manager, Marcel Brands, said the deal was a "record transfer fee for PSV" in a statement.
Reports are suggesting that fee is thought to be around 37 million pounds.
Gakpo will now travel to England imminently to finalise the deal with Liverpool and it is expected that he will be officially unveiled on New Year's Day, meaning he could be in line for his debut against Brentford on January 2.
