His paternal great-grandfather Agha Mehfooz Jan was the governor of four Afghan provinces under King Amanullah Khan's reign and was also the King's first cousin, while his paternal grandfather Abdul Sami Khan served as the Deputy Inspector General of Police. His paternal great-great-grandfather, General Ahmed Jan, was from Afghanistan and a military advisor to king Abdur Rahman Khan. Adnan's father served as a Pakistan Air Force pilot, before becoming a senior bureaucrat and serving as Pakistan's ambassador to 14 countries. His father, Arshad Sami Khan, was a Pakistani Pashtun while his mother Naureen Khan was an Indian from Jammu. He was raised and educated in the United Kingdom.
Sami was born in London, England on 15 August 1971.