Neill, 31, only joined Everton from fellow Premier League side West Ham United at the start of the season but said he was now looking forward to moving next week.
"The move has come as a surprise to me," he said on Everton's website.
He also told Sky Sports: "I'm now delighted I'll be joining a massive European club with great ambitions for the season.
"It will be a wonderful new challenge for me. I'm absolutely delighted a club like Galatasaray will be my next team."
Neill joins compatriot Harry Kewell in Istanbul and is eligible to play against Atletico Madrid in the last 32 of the Europa League wich resumes next month after the winter break.
Neill signed for Everton on a free transfer in September after rejecting a new deal at West Ham where he was captain and has made 15 appearances for the Merseyside club.
He is still available to play in their league match against Manchester City on Saturday before leaving.
The former Blackburn Rovers player has 53 caps and joins Frank Rijkaard's second-placed side in Turkey for an undisclosed fee reported to be to about 750,000 pounds.
Galatasary, who have won the league title twice in the last four seasons, trail fierce rivals Fenerbahce by one point. They are the only Turkish side to win a European competition, having captured the UEFA Cup in 2000.
