The Austria international completed his move to the Britannia Stadium from Werder Bremen on Monday.
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"Marko is a player we have been aware of for some time and I’m really pleased we have been able to add him to our squad," he told Stoke's official website.
"He has played at the highest level in Holland, Italy and Germany and is keen to make his mark in England with Stoke City."
Arnautovic, who played for Twente and Inter prior to joining Bremen, becomes Hughes' fifth signing at the club after Erik Pieters, Marc Muniesa and Oussama Assaidi all arrived, with Juan Agudelo set to join in January having signed a pre-contract agreement.
The striker has been capped 27 times by his country, scoring seven times.