The 26-year-old, a former Birmingham player and England Under-21 international, has been charged with betting on a competition in which his team plays, which is contrary to FA regulations.
It is understood that there is no suggestion of any match-fixing allegations or that Jerome has gambled on games he has been involved in.
"Cameron has admitted the charges and will in due course attend an Independent Regulatory Commission, at which he will be supported by the club.
"The club or the player will not be making any further comment at this time."
Jerome is facing the prospect of a ban - in June, Tottenham midfielder Andros Townsend was fined £18,000 and banned for four months, three of those months suspended, for similar offences. The charges meant that he missed playing for England Under-21s in the European Championships after he withdrew from the squad.
An FA statement said: "The FA has charged Stoke City's Cameron Jerome with breaches of its Rules in relation to a number of betting offences.
"Jerome has admitted the charges. A date for an independent regulatory commission to hear the case will be set in due course."