“Inter and the player have agreed to make Wesley Sneijder a Galatasaray player,” the Istanbul side said in a statement.
“Further statements will be made once the signing of contracts and medical examinations take place. Additionally, we will notify when the player arrives at the club.”
Sneijder had been marginalised at Inter after refusing to take a pay cut on reported £200,000 per week wages.
The former Real Madrid and Ajax playmaker, who was a stand-out player at the 2010 World Cup, had also been linked with Liverpool, although there was no evidence of a concrete offer from the English club.
He was offered his bumper deal by Inter in autumn 2010 to fend off reported interest from Manchester United, but the Premier League leaders were not interested this time out.
He said he hoped to make his debut in the Istanbul 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 started his career at Ajax in his native Netherlands, making 180 appearances for the Amsterdam club before sealing a 27 million euro move to Real Madrid in 2007.
He was not an automatic first choice at Real and, after falling out of favour at the Bernabeu, moved to Serie A with Inter in 2008.
That was a far more successful time for the Utrecht-born attacking midfielder, who led the Nerazzurri to the Serie A and Champions League titles in 2010 as Inter sealed a famous quintuple.
After making his international debut in 2003, Sneijder has won 90 caps for the Oranje and was a key player in their run to the 2010 World Cup final, where they were beaten by Spain.
But his career has since suffered from injuries and the contract dispute, with both club and player left to rue the decision to agree a huge salary that proved excessive for the Milan-based giants.