The 29-year-old told the club's website he was focussed and ready to face Wolverhampton Wanderers on Tuesday.
"At the end of the day, I sat down with my family, I sat down with the people around me and I said stop all this talking, stop all this waiting, I'm going to go the coach and tell him 'I'm ready to play'", he said.
"I'm back and I can focus now completely on West Ham because I have committed to stay and I'm going to give everything."
Arnautovic, who joined West Ham from Stoke City in 2017, said it had been a difficult time with speculation about his future swirling around.
"I said yesterday on my Instagram page that obviously it was a big offer, an interesting offer and me and my family took some time and thought about this because I think any human being would think about this," he said.
(Reporting by Martyn Herman; Editing by Peter Rutherford)
