Having already smashed the world transfer record with the arrival of Neymar, PSG pulled off another coup by landing Mbappe from their Ligue 1 rivals.
The teenage wonderkid moves on an initial one-year loan, but with a compulsory purchase option that will push the total transfer value to a whopping €180 million.
Vasilyev, who ironed out the details of the transfer along with PSG and Mbappe's representatives, has now affirmed that he cannot fathom how the buyers have stayed within the financial limits stipulated by UEFA.
"It was a very tough transfer. At the start, we didn't want to let him go to a direct competitor, but I've always shared a good relationship with his father who is also his agent. They convinced me," the Russian explained to TASS.
"But the talks with Paris were very complicated. We couldn't understand how they could sign the player without breaking FFP."
Ultimately, however, Vasilyev explained that the offer was just too good to refuse.
"It was a deal between three parties. The Mbappes always said that it was going to be done by the best terms for us," he added.
"Paris paid the price we asked, which was as much as we got from other European clubs".
The principality club saw a host of top talents leave over a lucrative summer.
As well as Mbappe, the likes of Benjamin Mendy, Bernardo Silva and Tiemoue Bakayoko moved on from the Champions League semi-finalists.