The Dutchman, 33, has signed a three-year deal and re-joins new Toffees boss Ronald Koeman after they worked together at Ajax and Southampton.
"Koeman is one of the best coaches. He is straight talking, fair and has confidence in me which counts as well," Stekelenburg told the club's website.
Stekeleburg twice won the Eredivisie title and has 54 international caps.
He spent last season on-loan at St Mary's, making 25 appearances, and has also had spells at Serie A side Roma and Monaco in France.
Koeman added: "I know through his professionalism, hardworking approach and personality he will fit in well with what I will be building at Everton."
Everton have signed goalkeeper Maarten Stekelenburg from Championship side Fulham for an undisclosed fee.