Onyeama, an accomplished writer, obtained his school-leaving certificate from Eton in 1969, according to the BBC.
He documented his experience in racial Britain in a book and was subsequently banned from visiting the school.
But Henderson said, “We have made significant strides since Onyeama was at Eton but – as millions of people around the world rightly raise their voices in protest against racial discrimination and inequality – we have to have the institutional and personal humility to acknowledge that we still have more to do.”
He said he would invite Onyeama in order to apologise in person and “to make it clear that he will always be welcome at Eton”.
“We must all speak out and commit to doing better – permanently – and I am determined that we seize this moment as a catalyst for real and sustained change for the better,” the headmaster added.
However, Onyeama said the apology was unnecessary and did not change his view of Eton, which on the whole was positive.
The writer, who earlier said he had been taunted on a daily basis at Eton by fellow students, added that the apology “compels the recognition that prejudice on the grounds of colour or race dehumanises its victims in a way that ordinary forms of prejudice do not”.
Eton has a reputation for educating some of the highest-ranking members of British society, including Prime Minister Boris Johnson, who is the 20th British prime minister to have attended the school, as did Archbishop of Canterbury Justin Welby and both the Duke of Cambridge and the Duke of Sussex.