The deal is worth €25m including various bonuses, plus Genoa will receive 10 per cent of any future transfer fee.
“I have signed the contract, yes," he told Sky Sport Italia.
“I am very happy to start this new adventure. I haven't had the chance to speak to the Coach yet, but I will do on Tuesday before the training session."
Pellegri completed his medical in Monaco this morning and was then whisked away to the Stade Louis II for the signing ceremony.
It's a five-year contract, reported to be worth €1m for the first season.
“I am not interested in money, as I just want to play and enjoy my football. If people had told me a year ago that I'd be moving from the Genoa youth team to Monaco, I'd have thought it was a dream, but this dream has come true.
“I thank Genoa for everything they did for me, but the time has come for us to part ways."