Neymar's arrival was announced on the Puma website alongside the banner "The king is back" and "Welcome to the family Neymar JR."
The 28-year-old Brazil international wrote in a statement on his Twitter page: "At the beginning of each new season, I take some time to think about my career and the choices I have made. I think about the dreams I had when I started this sport, and the path that lies ahead.
"This will be a different season, a special season. For that reason, as I have done in the past, I decided to write this text.
"I am about to live a unique experience, a new challenge. I consider myself privileged to have had a life filled with unique experiences and wonderful challenges.
"I grew up watching videos of great football legends such as Pele, Cruyff, Matthaus, Eusebio and Maradona ... These were the kings of the pitch, the kings of my sport. And they had something in common -- a love of the game, a drive to be the best version of themselves and a spirit that unites all. It's not always about being the best or the greatest but instead, to inspire future generations. That is exactly what I have dreamt of for myself, to give all of me to football because football has given me everything I have. I want to do it my way, using my gift.
"New challenges, new responsibilities, I understand that. I wish to bring back the legacy that those athletes created on the pitch. I was to help bring back memories from each of their football histories and the magic they gave us in their classic leather boots -- and through boots like those, leave behind my own legacy. They each played in PUMA, and each of them created their magic in The KING.
"And so now, as I begin this new season, I want the KING to reign on the pitch and inspire generations as it has inspired me and others.
"To be in this project, associating myself to those Kings of football, through KING, it is a dream. For these reasons, from today onward, I have the honour to unite with the brand that helped the biggest legends of football become what they are. Every time I lace my boots, my KING boots, I will do anything to achieve all of my dreams to honour my name and that of all those great ones who wore the KING before me. This will be my PUMA history. The KING is back!"
Sources told ESPN that only four executives knew about the deal to land Neymar and it was "a big secret in the company" that they had been working to sign the player for several months.
Neymar joined PSG from Barcelona in 2017 for a world-record €222 million fee and has won three Ligue 1 titles in Paris. He also helped the French club reach the Champions League final in August, where they were beaten 1-0 by Bayern Munich.
During his time at Barca he won the Champions League, FIFA Club World Cup and two La Liga titles.