The 23-year-old forward will officially become a Reds player at the start of the January transfer window after agreeing personal terms and successfully completing a medical at the AXA Training Centre.
Gakpo arrives on the back of an impressive World Cup showing with the Netherlands, netting three goals in five appearances, starring alongside Virgil van Dijk in helping their country reach the quarter-final stage.
Prior to the Eredivisie's pause for the Qatar tournament, he was the league's leading scorer and assister with nine and 12 respectively.
He told Liverpoolfc.com: "I feel really good, I'm really excited to be here. I'm looking forward to start training and start playing for this amazing club.
"I think this is a great club for me to come in and try to show what I can [do] and try to help the team to achieve more beautiful moments that they already did in the past years.
"I think for me personally it's also good to develop here and there's a lot of great players here [who] I can learn a lot of things from."
Born and raised in Eindhoven, Gakpo is a product of PSV's youth system, progressing through the ranks before making his senior debut in February 2018.
He went on to make a total of 159 appearances for his hometown club across all competitions, scoring 55 times. One of those secured the KNVB Cup in April 2022, the winner in a 2-1 triumph over AFC Ajax.
His rise at PSV would bring international recognition and, after representing the Netherlands at age groups U18 to U21, a first senior cap came as a substitute during the Euro 2020 group-stage fixture with North Macedonia in June 2021.
To date, Gakpo has tallied 14 appearances for his nation, with six goals scored.
He will wear the No.18 jersey at Liverpool.
He added: "I'm really looking forward to [playing at Anfield]. I heard a lot of great stories about the stadium, about the atmosphere. I cannot wait.
"Obviously [my aim is] to win as many prizes as we can as a team, to perform well, to show the world what we can do as a team and what I can do as a player. And personally, just to keep developing and become a better player every season.
"I'm really thankful that everybody is giving me such a warm welcome and I'm really looking forward to seeing everybody in the stadium and around the city."