The 37-year-old Bosnia & Herzegovina international will be one of their backups this term.
The ex-Toffee will be working with Jordan Pickford and the other goalkeepers at Finch Farm.
He previously played for the club between 2021-2023, while he spent five years at Stoke City.
Begovic told evertonfc.com: “I’m delighted to be back. It was an easy decision when the call came. I had two really good years here before and built special relationships with the staff and players.
“Everton has a way of leaving an imprint on you. The relationship I have with people here, how special the Club is, the amazing fanbase, and with it being such a significant last season at Goodison means it’s a great time to be at the Club.
“I’m looking forward to working with the keepers here again. Jordan a friend of mine for three years now and is someone I really respect. With Joao Virginia, Harry Tyrer, Billy Crellin and our Goalkeeper Coach, Billy Mercer, it’s a great group. The way we push each other on a daily basis brings the best out of us on matchdays.
“I want to help be a leader, set standards, be a pro every single day and pass on my experience. I can’t wait to be a part of it again and help the Club any way I can.”