The English manager has been the catalyst for Arnautovic's transformation from an inconsistent winger into the 'Hammers' talismanic out-and-out striker, which has seen him score nine goals since December.
The resurgance has been one of the key factors in guiding West Ham to the verge of Premier League safety with the club six points above of the drop zone ahead of a crunch match with strugglers Stoke on Monday.
Although Moyes admits he had his doubts about Arnautovic at first, he is now delighted with the form and attitude of his Austrian forward.
He told 'Sky Sports': "I was concerned, because I'd seen him play for Stoke sometimes and I didn't think he did all the running back defensively.
"We had to find a way of getting Marko into a different system. And we played around with it, it wasn't rocket science.
"We didn't go out there with it really planned. He was the one that showed us, and going to centre-forward freed him up a little bit. I got him to run and close things down, and show that he really had that capability.
Moyes continued: "He is a little bit of a Zlatan (Ibrahimovic) inasmuch as the players look to him. He's got a leadership role which he needs to develop as well, for the club and for the team.
"He's getting to an age now where he's going to influence players, and he's going to have to influence players around him, so he needs to be doing it by his leadership and performance. His performances have done it in many ways."