The deal was signed just hours after the 25-year-old paid off his 222 million euro (USD 264 million) buyout clause to Barcelona.
"I am extremely happy to join Paris Saint-Germain," said Neymar.
"Since I arrived in Europe, the club has always been one of the most competitive and most ambitious. And the biggest challenge, what most motivated me to join my new teammates is to help the club to conquer the titles that their fans want.
"From today, I will do everything I can to help my new teammates, to open up new horizons for my club and to bring happiness to its millions of supporters around the world."
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PSG said that Neymar will be unveiled at a press conference at the club's Parc des Princes at 1130GMT on Friday.
He will then be presented to fans at the same ground at 1345GMT on Saturday before the season-opening Ligue 1 fixture against promoted Amiens.
Leading coaches such as Arsenal's Arsene Wenger and Manchester United's Jose Mourinho lamented that the move could cause even greater inflation in transfer fees and player wages.
"It also looks like the inflation is accelerating," said Wenger, whose 21 years at Arsenal have been characterised by prudent spending.
"It's beyond calculation and beyond rationality."
However, in the French capital there is huge excitement at PSG's Qatari-backed project having landed a star name to finally make them feared among European football's elite with even French president Emmanuel Macron enthused.
"Neymar to PSG -- the transfer of the century", splashed Le Parisien's front page on Thursday with the first five pages devoted to his impending arrival.
The mood is understandably more sombre in Barcelona where attention has turned to who the Catalans can sign to replace Neymar in the month before the transfer window closes.
Neymar's Brazilian international teammate Philippe Coutinho of Liverpool and Borussia Dortmund's Ousmane Dembele have both been linked.
There is also scepticism at the role played by PSG's owners Oryx Qatar Sports Investments (QSI) at a time of political crisis for the energy-rich state which has been boycotted by its Gulf neighbours in recent months and will play host to the World Cup in 2022.
But whilst La Liga protests at losing one of its biggest stars, Barca's players have continued to wish their now former teammate well.
"My friend I wish you the best in everything that comes!!!" Luis Suarez posted on Instagram alongside a picture of the two hugging.
"Also thank you for your support, for everything that I learned with you and for the unique moments that we spent together!!!! Keep like this and never change love you little bro."
Earlier Thursday, Spain's football league threatened to stall the saga by initially refusing to accept the cheque presented by Neymar's representatives at its Madrid headquarters.
Clubs can be sanctioned by European football's governing body for making a loss of more than 30 million euros over a three-year period.
However, UEFA insisted the move will not automatically trigger a failure to comply with FFP regulations.
"The transfer of Neymar to PSG will have an effect on the club's finances over several years but the impact of such an operation cannot be judged in advance, notably as PSG could well sell several players for a significant amount," UEFA said in a statement to AFP.
"The club will pass on to UEFA the details of the above operation so that they can determine the disciplinary responsibilities that may arise from this case," continued the Barca statement.