Gakpo, who scored three goals for the Netherlands at the World Cup, joined Liverpool from PSV Eindhoven on Wednesday for a reported initial fee of 37 million pounds.
British media reported Manchester United were also chasing Gakpo before Liverpool sealed the deal.
"He's a really good player so the package is interesting," Klopp told reporters ahead of Friday's game against Leicester City. "Big for him. Big for us. Great day...
"He's a young player with a lot of potential. If he had been in a different position, scoring 40 goals, not in Holland but maybe in Spain, he would have been unaffordable. In these things, it's about timing and getting players in at the right moment, when they haven't scored 55 goals a season.
"We were following him, and he always kept making the next steps. We believe in our process, when offensive players come here, they all make a step forward because of the way we work and can help them."
Following his move to Anfield, Gakpo said he had been persuaded to join after speaking with Netherlands and Liverpool defender Virgil van Dijk (31).
"It was a home run (the negotiations)," Klopp said. "We didn't need Virgil to convince him but he likes to be involved in these things!"
Klopp said there were no new injuries in his squad, but suggested that the injured duo of James Milner (36) and Roberto Firmino (31), who missed this week's win over Aston Villa, would not recover in time to face Leicester.
He added that France defender Ibrahima Konate (23), who played in the World Cup final defeat to Argentina, had returned to training and is available for selection.
Liverpool, who are sixth in the league with 25 points from 15 matches, face a Leicester team that were outclassed by Newcastle in a 3-0 defeat on Monday, and Klopp said he expects a reaction from Brendan Rodgers' side.
"They could change their system which makes it more difficult," Klopp said. "But we have to push through what we want to do - it's been a long time since we played at home."
