The allegations were made against Edinburgh-based Fettes College, a £36,400-a-year boarding school which counts ex-prime minister Tony Blair among its alumni.
The school said racism by staff or students in any form was not tolerated and that inclusion was a “core value”.
Saffy Mirghani, who attended the school from 2011-13, told The Edinburgh Evening News that a so-called "slave auction" was organised each year by pupils where prefects would volunteer themselves as "slaves" and could be bought for charity by other pupils who could then "control them". The auctions were reportedly stopped in 2013.
"The slave auction just allowed the most disturbing and nefarious qualities and the most troubled students to percolate to the surface,” she told the paper.
"It was really quite frightening because it's a topsy turvy world where the saner students realised the practices and behaviour to be strange and were quietly whispering 'is it not weird there is a slave auction?' and feel they don't have a right to openly condemn it, whereas people engaging in insane behaviour are doing it openly."
She said there was a "culture of racism" at the school and claimed it was "endemic" to students and staff.
Geordie Milne, a white male prefect who was in Ms Mirghani's year group, claimed “casual racism was widespread and normalised”.
Femi Babbington-Ashaye, who was in the year below Ms Mirghani, told the paper how he recalled one male pupil saying: “I will make Femi my slave.”
Nian Li, a British Chinese student who was a boarder at the school from 2009-2015, said she was mocked by other pupils during an art class over the shape of her eyes in childhood photos she brought in for a project.
A Fettes College spokeswoman said: "Racism in any form by staff or students is not tolerated at Fettes and it is distressing to read these accounts from former students.
"Inclusion is a core value of the school about which we will never be complacent.
"The work of the student-led Fettes Equality Society, combined with that of the staff-led Equality Group, aims to ensure that diversity and inclusion across race, sexuality, gender and disability in the school is understood and enacted by all in our community.
"They meet regularly to discuss all school policies, to educate and to organise training for both staff and students.
"We would encourage any former student to contact the college to discuss their concerns directly and openly, so we can learn from their experiences."
Additional reporting by PA
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