The 31-year-old has spent the last two seasons on loan in Turkey and made the move permanent this week for an undisclosed fee.
Yobo told Everton's official website: "I would love to thank Everton and the management of Fenerbahce for reaching a deal.
"My family have settled well in Turkey and enjoy the life there, so I'm glad they will be re-uniting with friends here.
"It's been a long journey into achieving this dream and now is the time to pay the club and fans back with a great performance."
Yobo was signed permanently by Toffees manager David Moyes after an impressive loan spell in the summer of 2003 and played over 250 times for the club.