Arnautovic arrives at the Britannia Stadium after three years in Germany with Bremen which saw him score 14 goals in 72 appearances for the Bundesliga outfit.
The 24-year-old was involved as a substitute for Bremen in a 4-1 defeat at Borussia Monchengladbach on Saturday, but less than 24 hours later Stoke had agreed personal terms with the forward.
Stoke used their Twitter account to announce the signing with an image of Arnautovic wearing the club's home shirt.
The short accompanying message read: "Stoke City are delighted to confirm the signing of Marko Arnautovic from Werder Bremen."
West Ham United were also consistently linked with Arnautovic, who can play out wide as well and joins the Premier League with 27 caps for Austria to his name.