Varkey was born in Kerala, India in 1957. His Father, KS, and mother, Miriamma, were Kerala Christians, educators. The family moved to Dubai in 1959, when the emirate was still very undeveloped. His Father worked for British Bank of the Middle East, and both of his parents taught English to local Arabs, including members of the royal family. At the age of four, Sunny was sent back to Kerala to attend Infant Jesus School, a Catholic boarding school in Kollam city. When he was 11 years old, he sold fruit on the side of the road to make a little extra money. He and his elder sister returned to Dubai in 1970, and Sunny completed his O-Levels at St. Mary's Catholic High School. He pursued his A-Levels at Bembridge School in the UK for a year, and completed his A-Levels in Dubai at the British Council.