Navas, who signed for Real from Levante in 2014 and was the starter as Los Blancos won three consecutive Champions League titles, lost his place to Thibaut Courtois following his arrival from Chelsea last summer, even though the Belgian is yet to fully convince at the Bernebeu.
Navas, 32, was on the bench for Real in their 2-2 draw with Villarreal at the Estadio de la Ceramica on Sunday night, but said goodbye to his team-mates after the game according to a number of reports in Spain.
Navas, as quoted by the Evening Standard, said: “I’m really excited to sign for Paris Saint-Germain. After my experience in Spain, I’m coming to France with high hopes.
“Paris Saint-Germain is a very prestigious club in Latin America and I am keen to be part of the adventure that started several years ago.
“I will do everything I can to help PSG win new titles, bringing all my experience and professionalism.
“And I will also try to win the hearts of the Parisian fans, famous throughout Europe for their passion.”
It is understood PSG will pay around €15million for Navas, with Alphonse Areola moving to Madrid on loan for the 2019/20 season.
Navas leaves the Bernabeu after five seasons and 162 appearances under his belt, adding one La Liga title and one Spanish Super Cup to his three Champions League titles won.
Paris Saint-Germain face a striking crisis with Kylian Mbappe ruled out for four weeks and Edinson Cavani for three weeks after both came off injured in Sunday’s 4-0 thrashing of Toulouse.
France’s World Cup 2018-winning superstar Mbappe hurt his left hamstring doing a trademark sprint at Parc des Princes.
The issue means he will be absent for their opening Champions League group game, which is set for September 17 or 18. The 20-year-old will also be unavailable to Les Bleus for Euro 2020 qualifiers against Albania and Andorra early next month.
Fellow attacker Cavani hurt his hip in the same match and the Ligue 1 holders confirmed the Uruguay international will be out for three weeks, meaning he could be ready for European action.
The problems come at the same time as uncertainty surrounds the future of Brazil forward Neymar.
The Brazilian has sat out the opening three Ligue 1 fixtures because of his desire to return to La Liga. But there is only a week left before the European transfer window closes, meaning former club Barcelona and Real Madrid must move fast.
Even if the 27-year-old remains in Paris, he’s banned for their first three UCL fixtures.
Neymar’s future in Paris took another twist on Sunday after both Edinson Cavani and Kylian Mbappe hobbled off injured in Paris Saint-Germain’s 4-0 thrashing of Toulouse.
The Ligue 1 champions bounced back from a shock defeat to Rennes on the opening day but were left to count the cost with Uruguayan frontman Cavani and French hitman Mbappe both coming off.
Should either or both face a lengthy spell on the sidelines, PSG may well reconsider any willingness they might have for letting Neymar leave the club in the final days of the transfer window. And new midfielder Idrissa Gueye is among those who hopes the Brazilian will stay in Paris.
“I have no idea if he will stay,” said the Senegalese, who arrived this summer from Everton.
“For me it’s a pleasure to play alongside great players like him. Any team would like to have a player like him.
“I’m not sure what’s going on between him and the club. But as a player, he’s a great guy who bring a great atmosphere in the locker room and does the right things on the pitch during training.”