Edward Bunyan and Indira Gainiyeva, both 16, are thought to have vanished at around 3am from Stonyhurst College in Clitheroe, Lancashire.
It is thought they ordered a taxi together to Manchester airport, where they caught a flight to the Dominican Republic.
One report said that police were searching for the couple in the Caribbean, and quoted a school spokesman who said the two families were "desperately concerned".
Victoria Bunyan, the widow of Edward's older half-brother Christopher, said: "I don't approve at all but sounds like he is having quite an adventure."
She said he had heard of the disappearance on the news, adding: "It is going to get him in rather a lot of trouble I am sure.
"I'm not sure why he did it; they are very hormonal at that age. I don't know anything about the girl - I suspect her family are very worried too.
"I don't know what was going on at school for him but he is a bright boy so I am sure he will be ok and will work it out."
Fellow pupils took to social media - using the hashtags #WheresBunyan and #WheresIndira - to try and find news of their friends.
A Lancashire Police spokesman said: "We do know they are in the Dominican Republic but as to their exact location - inquiries are continuing to try and trace them."
Stonyhurst College, a Catholic day and boarding school, was founded in 1593, and proudly bills itself as one of Britain's leading Catholic boarding schools.
It received an outstanding inspection report in April 2010 from Ofsted.