The 53-year-old, who had been a free agent since being sacked as Spain coach last December, replaces Christophe Galtier after his departure from the club was confirmed earlier in the day.
Luis Enrique was unveiled by PSG at a press conference alongside the Qatar-backed club's president Nasser al-Khelaifi at their brand new training complex in Poissy, to the north-west of the French capital.
"I'm delighted to be joining Paris in order to enjoy a new experience," Luis Enrique said in a club statement.
"It's so exciting to meet new people, to live in this city, to learn a new language and, above all, to manage PSG."
The new coach, whose full name is Luis Enrique Martinez Garcia, is the eighth man to lead the club since the transformative Qatari takeover of 2011 and, like those before him, will be charged with bringing them the success in the Champions League that has so far proved elusive.
PSG have never won Europe's most prestigious club competition, coming closest when they lost in the final to Bayern Munich in 2020.
They have gone out in the last 16 in five of the last seven seasons, losing to Bayern at that stage in the campaign just finished. That defeat proved costly for Galtier.
Luis Enrique arrives with pedigree in the Champions League, having won it as coach of Barcelona in 2015 when a brilliant team led by an attack of Lionel Messi, Neymar and Luis Suarez beat Juventus in the final.
He now joins a club beginning their latest rebuild following the departure of Messi at the end of his two-year stay.
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Several high-profile new signings are expected to be confirmed as the club prepares to start pre-season training in the coming days, with a tour to Japan scheduled for later this month.
Luis Enrique brought to an end a three-year stay at Barca in 2017 and then became Spain coach in 2018.
However, he quit in June 2019 and announced the death of his nine-year-old daughter from bone cancer two months later.
He returned to the Spain post in November of that year, retaking the reins from Robert Moreno, and took La Roja to the Euro 2020 semi-finals and the 2021 UEFA Nations League final before being fired after their elimination from last year's World Cup in the last 16 in a penalty shoot-out against Morocco.
Galtier had only been in charge for one season and still had a year to run on his contract, but his departure had been expected ever since the end of the last Ligue 1 season a month ago.
"Paris Saint-Germain and Christophe Galtier have decided to terminate his contract as coach of the first team," the club said in a statement.
"Everyone at Paris Saint-Germain thanks Christophe Galtier, as well as his assistants Thierry Oleksiak and Joao Sacramento, for their professionalism and commitment over the course of the season, and wishes them the best in their future careers."
Galtier led PSG to a French record 11th title but that success was also overshadowed by their disappointing exit from the Champions League and a French Cup last-16 loss to Marseille.
The final weeks of Galtier's reign were also marred by accusations that he made racist remarks about players during his previous job at Nice.
He has vehemently denied the accusations but will stand trial in December on charges of "moral harassment and discrimination on the grounds of actual or supposed membership or non-membership of a particular ethnic group, nation, alleged race or religion", according to prosecutors in Nice.
The offences are punishable by three years' imprisonment and a 45,000-euro ($49,000) fine.
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