The 18-year-old right winger has signed a two-and-a-half-year contract with the Potters, with the option for a further year, after his short-term contract with West Ham expired at the end of January.
Stoke offered Fawunmi the contract on Tuesday after he scored twice and impressed in a trial match against Huddersfield Town’s B team which Stoke’s Under-21s won 4-2.
He had attracted interest from Greek side PAOK, who had tabled a three-year contract, but preferred to stay in England and now joins up with Stoke’s U21s.
Academy star Favour Fawunmi has joined Stoke City a week after leaving West Ham.
Standard Sport understands he had declined the offer of a new contract with the Hammers last month.