Alan Irvine has been appointed as assistant manager, while Charlie Adam will take on the role of set-piece coach.
Both moves were anticipated, with Moyes having previously confirmed his intention to reunite with Irvine and considering Adam for the set-piece role.
Speaking about the arrivals, Moyes said: "I'm delighted to have been able to add Alan and Charlie to our coaching staff. Obviously, Alan is somebody who I have known for a very long time and have tremendous respect for. His knowledge of the game, as well as his understanding of what is required at Everton – a club that means a lot to both of us – will be invaluable.
“Charlie is someone I have had several chats with since rejoining the club. He will be helping with set-piece situations, an area he excelled in as a player and one I believe he can really help us with now as a coach.
"The two of them, along with Billy McKinlay and Leighton Baines, give us a really strong coaching foundation as we look to make positive strides forward."