The 21-year-old is set to be swooped up by the free-spending French club this month having convinced the defender to join this summer
The centre-back was being chased by three clubs, according to his club's president, with the deal suspected to be sealed for around €5 million.
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.