The Bosnia-Herzegovina international has long been linked with a departure from the Etihad Stadium, having been unable to disldge Sergio Aguero as Manuel Pellegrini's first choice up front.
The Giallorossi stepped up their interest in Dzeko in July, with negotiations prompting him to be left out of the squad for a friendly between the two sides later that month.
Those talks appear to have progressed well as Roma announced the striker's touchdown in the capital on Thursday evening.
Pellegrini has Wilfried Bony still in his squad as support for Aguero despite Dzeko's imminent exit, as well as youngster Jose Pozo and new signing Raheem Sterling, who frequently played up front for Liverpool last season.
