While Arnautovic had a decent return of goals last season, he did not have the best relationship with his manager.
The Spanish striker joined the Gunners in 2016 for £17.1m from Deportivo, making 21 largely cameo appearances in 2016/17 scoring seven goals and five assists across competitions.
He said on West Ham's website: "I'm very excited and looking forward to achieving lots".
Current Premier League champions, the Citizens have signed Arzani, a 19-year-old midfielder who previously played for Melbourne City in Australia, a member of the same investment group as the English team.
"I'm very happy to be here at such a historic Club".
'I'd like to thank all of the people, the whole club, for having me'.
West Ham's Director of Football, Mario Husillos referred to Sanchez "a very experienced player whose career I have always followed closely and with admiration". But the Baggies are still hoping they can land the worldwide midfielder with the lure of playing in what could be a very exciting season as they battle for promotion back to the Premier League.
But the Hammers, who begin their Premier League campaign against Liverpool at Anfield this Sunday, do not expect anyone else to leave the club.