Osimhen, after last season's successful loan, joined Gala from Napoli in a permanent transfer this week.
Kavukcu, reflecting on the deal, revealed: "We have never compromised our position; we have demonstrated our strength.
"Thank God, we are not signing Victor's contract and leaving a debt for the future. This is an incredible source of pride for us; on the contrary, we have deposited Victor's contract as capital in Galatasaray's coffers.
"Think about it: it's insufficient to express it sufficiently, but the sums Victor has given up to come here are truly enormous. He has given up an amount that no other player would ever give up, and we are very happy to have him."
In their transfer statement, Gala declared they were paying Napoli €75m for Osimhen, plus a 10 per cent cut of any sell-in fee.
It was also announced that Osimhen had signed a four-year contract worth €15m-a-year, plus a €15.1m loyalty bonus and he would receive €5m-a-year in image rights.