Should PSG sign the France international on a permanent deal, his contract will run until June 2022.
Any deal for the 18-year-old is likely to be eclipsed only by the 222m euros (£200m) PSG paid for Neymar.
"I really wanted to be a part of the club's project, which is one of the most ambitious in Europe," said Mbappe.
The delay in signing Mbappe permanently is reported to be so PSG can comply with Uefa's Financial Fair Play rules.
The teenager scored his first goal for France in their 4-0 win over the Netherlands in World Cup qualifying on Thursday to become his country's youngest goalscorer since 1963.
Nasser Al-Khelaifi, president of PSG, added: "It was essential for French football that we keep and help develop such a great talent in our championship.
"Among players of his age, he is without doubt the most promising in the world due to his immense technical, physical and mental qualities.
"Since his emergence at the highest level, he has earned an excellent reputation as a young talent who is very respectful, open, ambitious and already very mature."