The Serie A side will visit on August 10, a week before the Potters open their Premier League campaign against Liverpool at Anfield.
It is the first time for four years Stoke have staged a high-profile home pre-season game.
"We were approached by a number of European clubs about the possibility of playing at the Britannia Stadium once we made it clear we would be staging a pre-season game at home," chief executive Tony Scholes told the official club website.
"Mark Hughes felt that Genoa would provide the right test at this stage of our build-up."
Stoke have also confirmed a friendly against Wrexham, Hughes' home town club, at the Racecourse Ground on August 4, three days after they return from their tour of the United States.
- Sports & Recreation
- Premier League