The Dutchman has agreed a three-year deal with Mauricio Pochettino's side ahead of the expiry of his Reds contract at the end of June.
The news officially brings the curtain down on Wijnaldum's five-year stay at Anfield, which saw him win the Premier League, Champions League, UEFA Super Cup and FIFA Club World Cup.
And that has prompted Klopp to highlight the 30-year-old's contributions to a glorious era in Liverpool's history.
“As a team we said our goodbyes to Gini at Anfield after the final game of the season. There was the public farewell on the pitch with the guard of honour. But then a more private occasion also,” Klopp said.
"It was difficult for all of us because of how much this astonishing person means to the group. He's been a big part of our lives for so long. There is nothing I won't miss about him."
One final Klopp hug for Gini at the Reds ❤️ pic.twitter.com/H4rrgDGPhQ— Liverpool FC (@LFC) June 10, 2021
Wijnaldum made 237 appearances for Liverpool across all competitions, scoring 22 goals.
"I will miss the player he is like crazy – highest-quality ability, one of the smartest players I have ever had the privilege to coach. His contribution was off the scale, a manager's dream," Klopp said.
"But as a person he'll leave just as big a hole. A more giving individual you could not wish to meet. Gini is very strong and opinionated, but his motivation is only to help the team – always. His team-mates adored him and respected him in equal measure.
"His smile lit up our workplace. He was a huge part of our beating heart. Of course, he is now someone else's and on behalf of the team we wish him great success in France with PSG.
"It is no surprise he's joined such an amazing club. Knowing his personality, he will fall in love with the city and the team – and they with him. Farewell, Gini: you came, you saw, you won the lot. You're a Liverpool legend now and forever."