Spread over 49 acres, the school was built at a cost of Rs 176 crore, the state government said.
The school, established with the mission of "Yuvaaon ko Shiksha, Desh ki Raksha," will offer residential education for boys and girls from classes 6 to 12.
Chief Minister Yogi Adityanath was also present during the inauguration.
Earlier in the day, Adityanath welcomed Dhankhar following his arrival at Gorakhpur airport.