Sneijder confirmed that he agreed terms in a live telephone interview with Galatasaray's website and said he hoped to make his debut in the derby against Besiktas in one week's time.
"It will be amazing and the atmosphere will be nice, I can't wait to go there and play my first game," said the 28-year-old.
"I will make the Galatasaray fans very proud and very happy. I'm looking forward to meeting them and making a good life together."
Sneijder was one of the world's outstanding players in the 2009/10 season and, although he has failed to maintain those heights, his decision to move outside the top five European leagues is still likely to surprise many critics.
A free-kick specialist, Sneijder joined Inter in 2009 after two seasons with Real Madrid and helped them win a Serie A, Champions League and Italian Cup treble in his first season in a side coached by Jose Mourinho.
He also helped Netherlands reach the World Cup final in 2010, beating Brazil on the way.
He is the latest big name to abandon Italy's ailing Serie A after Zlatan Ibrahimovic and Thiago Silva left neighbours AC Milan in the close season and Ezequiel Lavezzi departed Napoli.
Sneijder and Inter fell out in December when the club asked him to extend his contract from 2015 to 2016 for the same overall payment in a move criticised by the world players' union FIFPro.
Since then, the 28-year-old has been left out of the Inter team although coach Andrea Stramaccioni has said his exclusion was due to technical reasons.
Sneijder has only played three Serie A games this season.
Galatasaray are top of the Turkish Super League and face Besiktas on January 27. Sneijder said he expected to arrive in Istanbul and be officially presented to the supporters on Monday.
"I will be ready for that game," he said.
