Arteta's quality can be summed up by his 92.4% pass completion rate - the second best in the Premier League this term.
Moyes said: "Mikel's been great. He was great for Everton.
"We really enjoyed having him here. He was a great boy and I think he's done well for Arsenal.
"He's been an important cog in their team, he's one of the highest passers in the league. He doesn't give the ball away very often. So I think he helps their style and he's important for them."