The move comes after Antoine Kombouare left the post earlier on Friday, marking a return to the touchline for Ancelotti for the first time since he was sacked by Chelsea in May.
Ancelotti was pictured meeting PSG sporting director Leonardo in the French capital on Wednesday before Friday's confirmation he will take over the Ligue 1 leaders.
The deal, which took some time to put together, was confirmed after PSG revealed Kombouare had left the post just an hour before Friday's press conference, which Ancelotti attended.
Kombouare was constantly at the centre of scrutiny this season despite leading PSG to the top of the Ligue 1 table at the winter break.
However, the 48-year-old oversaw a premature Europa League exit at the group stage, which did not fit in with the club's ambitious new Qatari owners, who have sought to reinvigorate the capital club with high-profile names.
Ancelotti, 52, fits that bill and the former AC Milan boss could also be joined by David Beckham, who he coached briefly at the Italian club during his first loan spell at the San Siro, in the coming days.
PSG are reportedly close to completing a deal to sign the former England skipper once his contract with Los Angeles Galaxy expires at the end of the month.
Ancelotti won a league and cup double with Chelsea in his first season in charge before he was sacked at the end of last season despite finishing second.
The Italian was also a two-time Champions League winner during his decade-long spell at Milan.
Ancelotti has joined PSG in a reported two-and-a-half year deal and will face former club AC Milan in his first game in charge in a friendly on January 4 in Dubai.
"I want to do a great job," Ancelotti told reporters.
"I am delighted to be here as coach of Paris Saint-Germain. I think PSG is a fantastic club. I think I can do a great job to help PSG become a big club in Europe.
"The club has everything to succeed and enormous ambition.
"I will do my best to learn French in the best possible way, although I'd rather continue to speak in Italian."
PSG sporting director Leonardo denied there is any update surrounding the speculation that Beckham might be joining the Ligue 1 club.
"We have never said it was done," Leonardo said.
"We have a good relationship but I don't know what he is going to do.
"There is always the question of his personal life. He is in Los Angeles.
"Nothing is signed."
Ancelotti also confirmed that Claude Makelele will be his assistant coach.