Mario Dzhambazov, from Bulgaria, pleaded guilty to two counts of causing death by dangerous driving following the collision on the roundabout junction with Middlesbrough Road and the A171 at Guisborough.
The 18-year-old also pleaded guilty to driving without insurance at Teesside Crown Court.
Michael Liddell, 68, and his daughter, Sarah Liddell, 41, sadly died following the incident on Thursday June 13.
Dzhambazov, of Abbots Road, Whitby , appeared via video link from HM Prison Durham
He has been remanded into custody until he appears for sentencing on September 9.