The combative midfielder had been a target of Middlesbrough last season but instead went on loan to Borussia Dortmund from Real Madrid.
Flavio emerged as a key target of Galatasaray this summer - and lengthy talks with president Ozhan Canaydin have proved fruitful.
"I'd like to announce to the club and its fans that we have reached an agreement with Brazilian footballer Flavio Conceicao on all matters," said Canaydin on the club's official website.
Flavio had suggested that he would have liked to stay in Dortmund after his successful spell there - but it appears the prospect of a lucrative contract in Turkey has changed his mind.
