The 17-year-old male was due to appear at Edinburgh Sheriff Court following the crash in the early hours of Saturday morning on Greendykes Road.
The 16-year-old passenger remains in a serious condition in hospital after the car crashed into a wall near to the Wauchope House high rise.
A police spokesman said: "A 17-year-old male is due in court in connection with the incident.
"We would also like to reiterate our appeal for anyone who witnessed the crash to contact police."
Anyone with information about the incident should contact Lothian and Borders Police on 0131-311 3131 or anonymously through Crimestoppers on 0800-555 111.