Gakpo 23, was one of the World Cup revelation despite the Netherlands unable to progress past the Round of 16 against eventual winner Argentina.
Nevertheless, Gakpo scored 3 goals in the opening group stage.
Aside his adventures at the World Cup, he was awarded the Dutch player of the year, last season at PSV.
His goals met the criteria of Jurgen Klopp's striker and he is more clinical than Uruguayan Darwin Nunez.
He signed a long-term contract with an initial £30M with add-ons to take the deal to £50M.
? OFFICIAL: Liverpool have signed Cody Gakpo from PSV Eindhoven, the deal has been signed tonight between clubs. #LFC— Fabrizio Romano (@FabrizioRomano) December 26, 2022
Gakpo will sign long-term deal later this week as contract is fully agreed too.
Liverpool will pay £37m plus add-ons, up to £50m potential package. pic.twitter.com/JFSKL6zQKH
United had instigated talks but were still to finalise a financial offer and Liverpool have taken advantage.
Gakpo had offers from Leeds and Southampton last summer but chose to stay at PSV after the Dutch club rejected offers.
The 23-year old had chosen to wait for offers from clubs contending in the Champions League and despite the pull of United's Erik Ten Hag, Liverpool fit the bill.