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.

The discovery of oil in Dubai in 1966 brought in many foreign workers, including many from the Indian subcontinent; with the increased demand for an English-language education for the children of Indian expatriates, Varkey's parents founded Our Own English High School in Dubai in 1968. Varkey returned to Dubai in 1977, and his employment included work at Standard Chartered bank, opening a small trading company and a maintenance company, becoming part owner of the Dubai Plaza Hotel, and entering the Health care industry.

Varkey Group is the umbrella organisation covering GEMS Education and Varkey's other businesses, including Health care and, previously, construction. Varkey founded the company in 1979, and it is based in Dubai, with additional offices in the UK, U.S., and India.

When in 1980 local authorities insisted that his parents' Our Own English High School be housed in a purpose-built facility, Varkey took over the operation of the school, which had under 400 students at the time. He soon dropped his other businesses, expanded the school, and added new schools as well. The education situation in Dubai was ripe for expansion, since local schools were only for native Arabs, and the children of the ever-increasing number of expats needed education of their own. Varkey opened Indian, Pakistani, and British schools, and offered education under the different curricula: Indian (CBSE and ICSE), U.S., British, and later International Baccalaureate.

In 1984 Varkey founded Welcare, a Health care consultancy and management venture which developed a number of hospitals and clinics. A controlling interest in Emirates Health care, the Varkey Group's umbrella company which held Welcare, was purchased by Mediclinic International in 2012. The sale of his Health care sector allowed Varkey to focus on education and educational philanthropy.

After creating a strong network of schools in the Arab states of the Persian Gulf, in 2000 Varkey established Global Education Management Systems (GEMS), an advisory and educational management firm, in advance of his worldwide overseas expansion. In 2003, he began opening GEMS schools in England, beginning with Sherborne House in Hampshire and Bury Lawn in Milton Keynes. Soon afterwards, he took over Sherfield School in Hampshire, and purchased another 10 schools in England, mainly in the north.

In 2004, Varkey's GEMS group opened its first schools in India. Varkey continued to add schools in the subcontinent, and also purchased a controlling interest in the India-based Everonn Education, which the Varkey Group and GEMS manage. GEMS subsequently opened schools in Kenya, Uganda, Egypt, Jordan, Libya, Singapore, the U.S., Switzerland, and elsewhere around the globe. It is the largest operator of private kindergarten-to-grade-12 schools in the world, and as of 2014 has over 130 schools in over a dozen countries.

Varkey developed a habit of philanthropy from the Example of his Father and from his own strong spiritual values. In December 2010, he consolidated and structured his various donations and charitable initiatives by creating the Varkey Foundation (initially the Varkey GEMS Foundation) as the philanthropic arm of GEMS. The foundation intends to impact 100 impoverished children for every child enrolled at GEMS schools, via enrolment and education-access initiatives, worldwide Teacher training programs, advocacy campaigns, and physical projects such as building classrooms, schools, and learning centres. Bill Clinton launched the foundation.

In March 2011, the foundation partnered with UNESCO for girls' education in Lesotho and Kenya, and donated $1,000,000 to the effort. In September 2011, a further $1 million was pledged with UNESCO to train 10,000 school principals in India, Ghana, and Kenya. In 2014, the foundation's Teacher Training Programme committed to train 250,000 teachers within 10 years in under-served communities across the world.

In 2013, the Varkey Foundation helped launch the annual Global Education and Skills Forum, in partnership with UNESCO and the U.A.E. Ministry of Education. Bill Clinton gave the inaugural keynote address. Varkey hopes the annual forum will become the "Davos of education". At the second annual forum in March 2014, Varkey announced the Global Teacher Prize, a $1 million award to an exceptional Teacher who has made an outstanding contribution to the profession, to be presented at the third annual GESF in 2015.