The Republic of Ireland international was paraded to supporters at Goodison Park prior to their Barclays Premier League game against Norwich.
McGeady won four Scottish Premier League titles, two Scottish League Cups and two Scottish Cups in six years in the Celtic first team.
He was also voted Scotland's best player by his fellow professionals in 2008 before moving to Russia for £9.5m two years later.
The 27-year-old was expected to move to Everton at the end of the season, but Roberto Martinez has decided to strengthen his squad now after paying an undisclosed fee.
McGeady's switch to Goodison sees him link up with international team-mates Seamus Coleman, James McCarthy and Darron Gibson.