McGeady will be reunited with new Black Cats boss Simon Grayson, for whom he played 35 games, scoring eight times, at Preston North End last season.
The 31-year-old, who began his career at Celtic, joined Everton from Spartak Moscow in January 2014 and subsequently played 41 games, scoring once.
He has also made 90 appearances for the Republic of Ireland.
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Everton winger Aiden McGeady is to join Championship side Sunderland on a permanent deal.