The 21-year-old is set to be swooped up by the free-spending French club this month as the latest signing for the newly promoted Ligue 1 side.
The center back was being chased by three clubs, according to his club's president, with the deal suspected to be sealed for around 5 million euros.
Isimat-Mirin, though not yet officially a Monaco player, says refusing the prospect of playing for the newly promoted, cash-rich Ligue 1 club was impossible.
"I want to grow with [Monaco]," he told Telefoot. "I could not refuse such a project so I just decided to go."
The 21-year-old, who has featured for France Under-21s, will join the likes of Radamel Falcao, Joao Moutinho, James Rodriguez and Ricardo Carvalho as one of Claudio Ranieri's summer signings.