After weeks of negotiations, the clubs reached an agreement on transfer deadline day for a fee of €95 million ($102.6m), including add-ons, Eintracht said.
The 24-year-old has signed a five-year deal at PSG.
"We are delighted to welcome Randal Kolo Muani -- a proud Parisien and Frenchman -- to Paris Saint-Germain; to his city and his home," PSG president Nasser Al-Khelaifi said.
"We have worked incredibly hard to get this transfer over the line. Randal is a fantastic French international player and is committed to PSG and our project. I'm so excited to see Randal in a PSG jersey, giving everything for the Club.
Said Randal Kolo-Muani: "It's great to be back where it all began! I was attracted by the club's project. Now I can't wait to get to work and finally play in these colours."
The move comes after Eintracht said that Kolo Muani refused to train with the club earlier this week as he looked to push through a transfer to the French champions.
After joining Eintracht from Nantes, Kolo Muani impressed last season with 23 goals in 46 matches overall and started this campaign with three goals in four games.