The Serbia winger joined the Italian champions after the 2010 World Cup, but found opportunities limited under new coach Antonio Conte.
Fenerbahce were interested in landing Krasic on loan in January, but the former CSKA Moscow man was keen to seal a permanent switch.
Krasic is due to fly to Istanbul to be presented to the club's fans on Friday.
Fenerbahce are also set to complete the permanent signing of Nigeria defender Joseph Yobo, who has spent the past two seasons on loan at the Turkish club from Everton.
- 2010 World Cup