Neill, who agreed a one-year deal at Everton after his contract with the Hammers ended last year, made 15 appearances for the club.
"I'd like to thank the staff and fans but most of all my team-mates for making my time at Everton very enjoyable," he added. "I am pleased to have had a positive impact on the team and the club and wish them every success for the future."
Former Liverpool star Harry Kewell, a team-mate of Neill's in the Australia team, and ex-Aston Villa striker Milan Baros are already playing at the Ali Sami Yen Stadium.
Galatasary, who have won the league title twice in the last four seasons, currently trail rivals Fenerbahce by one point and are coached by Dutchman Frank Rijkaard.
Neill began his professional career with Millwall in 1995 before heading to Blackburn six years later for a £1m fee and then he signed for the Hammers in January 2007.
The Sydney-born defender last played for Everton in the 2-2 draw at Arsenal in the Premier League on 9 January.
He also led Australia in their successful World Cup qualifying campaign, which starts in June in South Africa.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.