Gakpo is set to cost Liverpool up to £45m, seeing off competition from rivals Manchester United for his signature.
Gakpo courted interest from Manchester United and Leeds United during the summer transfer window but a move failed to materialise.
His performances at the World Cup added the likes of Bayern Munich and Real Madrid to the conversation but it is Liverpool who have won the race to sign him.
Gakpo enhanced his status as one of Europe's best young players with an impressive display at the Qatar 2022 FIFA World Cup.
The 23-year-old scored three goals for Netherlands in Qatar as Louis Van Gaal's side reached the quarterfinals before losing to Argentina.
"PSV and Liverpool FC have reached an agreement on the upcoming transfer of Cody Gakpo," wrote PSV in an official statement.
"The 23-year-old attacker will immediately leave for England where he will undergo the necessary formalities to complete the transfer. Both clubs are not making any announcements about the transfer fee. 'But this is a record transfer for PSV,' said general manager Marcel Brands.
"The PSV management completed the transfer on Boxing Day and gave Gakpo permission to travel to England."
Gakpo has made 24 appearances across all competitions for PSV this season, scoring 13 goals and providing 17 assists.
