That took Mbappe's tally to four goals in seven games during Les Bleus' successful campaign in Russia, although it was not enough to edge out Luka Modric for the Golden Ball award.
There have been suggestions that PSG would have to offload the teenage sensation to one of Real Madrid or Manchester City to fulfil Financial Fair Play obligations, but the ex-Monaco striker wants to remain at the Parc des Princes.
"I will stay with PSG, continuing on my path with them," he told reporters after the final in Moscow. "I am at the beginning of my career.
"Scoring in a final is always unique. I have worked hard to reach moments like this, but this isn't the end, we must continue. I have the ambition to go further.
"I'm prepared for this kind of thing but then you have to prove it on the pitch. International football generates a lot of pressure, but if you are sure of yourself and surrounded by great players, you can do things like this."
Mbappe is thought to have cost PSG £120m to sign from Monaco, making him the second-most expensive player in the world behind clubmate Neymar.