He joins the Turkish giants on an initial two-year deal with an option to extend further for another year.
The deal was initially announced by Lyon before Istanbul Basaksehir also did the same on social media.
Rafael departed Olympique Lyonnais on a free transfer after the club agreed to mutually terminate his contract
which had just 12 months remaining to run.
The 30-year-old travelled to Turkey early on Tuesday morning to complete his move to the Turkish giants.
His entourage had been in conversations with a number of Turkish clubs, but it is Basaksehir who won the race for his signature.
A statement on the Istanbul Basaksehir official website said on Tuesday afternoon:
"Our club signed a 2 + 1 year contract with Brazilian football player Rafael. Our Vice President Mesut Altan and our CEO Mustafa Eröğüt took part in the signing ceremony of the successful defender"
"Rafael, who has played in important clubs in Europe such as Manchester United and Lyon, will wear the number 4 jersey in our club."
"We welcome Rafael to our family and wish him success with our orange-navy blue jersey."
Merci @orafa2 ❤️ pic.twitter.com/xhlzuc7MLI
— Olympique Lyonnais (@OL) September 8, 2020
The ex-Manchester United man spent five seasons with the club, making 139 appearances and scoring twice in that time-frame.
On the reason for his departure, He told Lyon bosses this summer that he wanted to start a new adventure where he could be guaranteed regular playing time.
Coming with lots of experience from all over Europe, Rafael is expected to feature on the right-hand side of defense for Okan Buruk. The Brazilian is also well known for his leadership abilities which will come in handy as well.
