Moyes is set to be presented as the new Sociedad coach on Thursday, seven months after he was sacked by Manchester United.
The 51-year-old sought advice from Arteta before agreeing to take the role at the Liga club, having signed the midfielder from Real Sociedad when he was in charge at Everton.
And Arteta believes his former manager can make a big impact in San Sebastian.
"I gave him my opinion about La Real," he told Cadena Ser
"He's a coach that likes to tighten the reigns, he'll do well with the group. He demands a lot and works hard, he's not what you'd call a 'typical' English manager that sits on the bench.
"He analyses a lot and he has a clear idea of how he wants his team to play.
"There are things [like the language barrier or knowledge of Spanish football] that could have an adverse effect, but when he made the decision to come to Real Sociedad over the other offers he had, it's because he sees their potential moving forward.
"If he's not able to get the team moving forward from the start, it's going to hurt him.
"I wish him the best, he's a coach that can light a fire under a player and the player will fight to the death for him. He's a coach that deserves it."
