A World Cup winner with France in 1998, Zidane won the Champions League as a player with Real in 2002.
As coach he had two spells in charge of Madrid, winning his hat-trick of Champions Leagues in his first stint as well as one La Liga title, two Club World Cups, two UEFA Super Cups and a Spanish Super Cup.
He walked out of Real in 2018 but was reappointed in March 2019 and won another La Liga title in 2020 before departing again the following year.
Zidane was in Paris at the same time as the Emir of Qatar for last month's Champions League final at the Stade de France, which was won by Real against Liverpool.
Earlier, PSG announced the arrival of Luis Campos as their football advisor to replace the departed Leonardo.
The 57-year-old Portuguese super-scout built the Monaco team that denied PSG the title in 2017 and knows Kylian Mbappe well as the striker was emerging in the principality at the same time.
Campos then became the genius behind the scenes at Lille, helping them build a team that pipped PSG to the Ligue 1 crown last year before departing.
"I am delighted to be joining Paris Saint-Germain, which I consider is the most ambitious and exciting club in world football," Campos said in a PSG statement.
"I believe strongly in and share the vision of the club and I cannot wait to get started to further unleash the great potential of this exceptional club."
The new French top-flight season begins on the weekend of 6 and 7 August.
A week before that champions PSG will play French Cup winners Nantes in the Trophee des Champions, the traditional curtain-raiser to the French season, in Tel-Aviv, Israel.