The Spanish playmaker, who was linked to a move away from Goodison Park, has pledged his long-term future to the toffees.
This has come as good news to Everton fans, after Tim Cahill also quieted speculation by commiting his future to the club. And Moyes is relieved that 28-year-old Arteta has rejected reported interest from Premier League sides, including Manchester City and Arsenal.
"Mikel is so important to us. He proved that when he came back last year from injury. I did not want to lose him and had no intention of selling him,” Moyes told reporters.
"But I had realistic fears he might go elsewhere, although not back to Spain. We try to do our best for the players and the chairman [Bill Kenwright] did well to convince him to stay with Everton."
Arteta is set to start in the game against Blackburn Rovers tomorrow at Ewood Park, where Everton kick off their Premier League campaign.
Cahill is also set to appear in the starting XI despite sitting out of Australia’s friendly against Slovenia in mid-week with a knee problem.
"I am really happy with the squad," Moyes continued.
"It makes me feel great I am not talking about a lot of injuries. If we had let our better players go we would have to rebuild.
"I know I don't have the money to go out and buy new players, so I have to try to keep our best ones. We have to be looking towards the top of the league. We have a good enough team, a good enough squad to compete. That will be my aim.
"Part of the manager's job is to raise expectations and there is quite a bit of expectation around Everton. But there is a tinge of realism as well as we look at what Manchester City and Tottenham are doing. It looks as though they are are going to have a good go at it, and it could be a tight Premier League with more emphasis on winning games."
Former Manchester United striker Louis Saha is favourite to start up front for the Toffees' opening league fixture, with Jermaine Beckford possibly on the bench.
Moyes is impressed with the progress of Beckford, who scored three goals in the club’s pre-season friendlies.
"He [Beckford] has terrific movement in and around the box. He offers us something different," said the Everton manager.
"He is a hungry player. He has come from non-league to Leeds. You hope he retains that hunger and remembers where he was not too long ago and how far he has come.
"I hope he shows that in his performances. What he wants to do is score goals and that's what he does. What we have seen so far in training, he is very good at it."
Ayegbeni Yakubu could be exiting the gates at Goodison Park after West Ham’s attempts to offer a substantial bid for the player.
"They made an offer of £6million, then £5million," said Moyes. "The price has gone down but Yakubu's record in the Premier League as good as anyone's."
He continued: "We have group of players that if they don't play well I can change them around.
"The team that starts the season may not be the one that starts the second or third game. We have also have a mixture of players who can play in several positions, which is good."