Sonic was born on a small island called Christmas Island. But his love for adventure called him away and he has visited so many different places on Earth that he doesn't really have a place he considers to be home.
— Sonic's backstory from
Sonic the Hedgehog Technical Files. Christmas Island ( is the place where クリスマス島 Kurisumasu tō ) ? Sonic the Hedgehog was born.  No other information is known or ever given about this island, nor it has ever been referred to in video game appearances or any other media, but it appears to be based on  one of several real-life islands of the same name.
The translation for the backstory was made by
Sega Technical Institute. It has also been featured as part of the limited Birthday Pack of during Sonic's tenth anniversary.
Sonic Adventure 2
Sonic Dimension - With original Japanese translation of the backstory (courtesy of archive.org)