The clubs held talks on Monday night as Liverpool moved to head off competition from Manchester United.
United had instigated talks but were still to finalise a financial offer and Liverpool have taken advantage, with PSV confirming that a deal had been reached between the two clubs.
In a statement on Twitter, PSV wrote: ‘PSV and @LFC have reached an agreement on the proposed transfer of Cody Gakpo. The 23-year-old attacker will leave for England imminently where he will be subjected to the necessary formalities ahead of the completion of the transfer.’
Last summer, Gakpo received bids from Leeds and Southampton, but he decided to stay at PSV after the Dutch club turned them down.
Despite the attraction of United’s Erik Ten Hag, the 23-year-old decided to wait for bids from clubs competing in the Champions League, and Liverpool filled the criteria.