The veteran midfielder joined the Parc des Princes outfit after being allowed to call time on his five-year stint with Chelsea.
The 35-year-old, who had a year remaining on his contract at Stamford Bridge, revealed the Londoners allowed him to leave the club to pursue his dream of joining his wife and son, who live in Paris.
"It's a very important challenge for me but also a very difficult one. I felt that my cycle at Chelsea was coming to an end.
"I'm coming to bring a little more experience. I'm not coming like a Messiah but to teach what I also learned when young."
The move to Paris will likely be Makelele's last, ending a career that has included stints in Spain and England.
However, the midfielder is not ready to end his playing days in the near future.
"People always tell me I'm 35. That doesn't bother me, I don't notice my age," he continued. "I still have the same energy on the pitch. If I can play until I'm 45 like that, I will.
"I have done a tour of the best leagues and now I'm back where it all began. It will be a good way to finish."