Wijnaldum has moved to the French capital on a three-year contract following the expiration of his Liverpool contract.
The 30-year-old spent five seasons at Anfield, having joined from Newcastle United in the summer of 2016 and won one Premier League title, one UEFA Champions League trophy, one FIFA Club World Cup and one UEFA Super Cup during his time at the club.
“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 told the club's official website.
"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."
"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 added.
"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."