The 32-year-old had six months to run on his £350,000-a-week deal but he is expected to forego a proportion of the £7m he is owed in wages so he can join Fenerbahce early.
Ozil said his Arsenal goodbyes on Sunday before flying to Istanbul last night.
A formal announcement on his free transfer to Fenerbahce is set to be made this week once his medical and the relevant paperwork have been completed.
“I am very excited because I was always a fan of Fenerbahce. My has dream come true for me,” Ozil told Fenerbahce’s club TV channel last night.
“That’s why I'm very excited to wear the jersey. I hope I will be successful with my teammates. I hope everything will be fine. I wish the best.
“God bless them (the fans). They always support it. We already know how big we are as a Fenerbahce community.
“They showed it again. I am so happy. I hope I can thank them on the pitch. I wish the best.”
Fenerbahce have been tracking Ozil for some time and the German has been regularly linked to the club he supported growing up. MLS side DC United have also had interest in Ozil’s desire to play for his boyhood club has helped Fenerbahce win the race to sign him.
The move brings an end to his time at Arsenal, who he joined for £42.5million from Real Madrid back in the summer of 2013.
Ozil has fallen out of favour under Mikel Arteta and he has not played for Arsenal since last March. He was also not registered by the Gunners in either their Premier League or Europa League squads this season.
He and his agent, Erkut Sogut, have previously been adamant he would see out his contract at Arsenal, despite his lack of football. But he has reached an agreement with the club to end his deal early, though the terms of his agreement with Arsenal have not been disclosed.
Ozil is expected to finalise his move to Fenerbahce over the coming days and the club’s sporting director, Emre Belozoglu, has said he is delighted a deal is close to completion.
“I say that Mesut’s childhood dream, and the dream of all Fenerbahce people, will come true,” Belozoglu said last night.
“Mesut is one of the biggest stars the football world has ever seen. We have a good, strong team. With Mesut’s arrival, I hope we will have very good days, win great trophies. We have two to three days ahead of us. Then we make the necessary announcements together.”
Ozil has insisted he is fit to play for Fenerbahce straight away despite not playing a competitive match for 10 months.
“I haven’t played a match in a while, but I am physically fit, I have no issues,” he said.
Arsenal play Newcastle tonight and the imminent departure of Ozil means Arteta can finally move on from an issue that has dominated the agenda in recent months.
Arteta is focused on what he hopes will be a bright future with young players like Bukayo Saka and Emile Smith Rowe, who are both expected to start this evening.
Kieran Tierney has recovered from the calf issue that kept him out of last Thursday’s 0-0 draw with Crystal Palace and is in line to return.