The veteran will play on next season as Blues captain after penning a new 12 month contract.
Moyes said: “Seamus is more than just a player at Everton. He offers so many different qualities.
“His leadership, his professionalism and his humanity are second to none. He’s helped carry the Club through some difficult periods in the past few years and his influence in the dressing room has been key to that.
“He's had to deal with some really difficult injuries, too, but he has done that and still been able to help inspire inside the dressing room at the same time.
“This could be a period of real change at the Club and I want somebody who can help deliver the messages of what it means to be an Everton footballer. Seamus has always done that and I know he will continue to do so as we move into a new era.”