According to media reports, the overall transfer fee could rise to 180 million euros including add-ons, which would make Mbappé, 18, the second-most valuable player ever behind his new teammate Neymar.
"Paris Saint-Germain is delighted to announce the immediate arrival of Kylian Mbappe," the club wrote on its website. "The loan agreement also includes an option to buy which, when exercised, will bind the player to Paris Saint-Germain until 30 June 2022."
26 goals in 44 matches
Mbappé burst onto the scene in the second half of last season and scored 15 goals in 29 appearances in Monaco's run to the French title. He netted 26 times in 44 matches in all competitions.
Brought up in the northern suburbs of Paris, Mbappé was compared to a young Thierry Henry as he first broke into the Monaco side in December 2015, just before his 17th birthday. He has won four caps for France.
"It was essential for French football that we keep and help develop such a great talent in our championship," said PSG president Nasser Al-Khelaifi at a press conference. "Among players of his age, he is without doubt the most promising in the world."
Mbappé, Neymar deals may mean sanctions
Also targeted by Real Madrid this summer, Mbappe's move to PSG will leave many wondering how the Qatar-owned club can avoid sanctions from European football's governing body considering the investment already made on Neymar.
The French club shattered the previous global transfer record when they splashed out a staggering 222 million euros to prise the Brazilian superstar away from Barcelona.
FFP rules currently stipulate that clubs cannot post losses of more than 30 million euros over the three-year period to 2018.
Among the sanctions risked by PSG if they are found to have broken those rules is a ban from the Champions League.
Mbappé netted his first goal on Thursday night, as France beat the Netherlands 4-0 at a World Cup qualifier.