Live to Lead will be broadcast only a few weeks after the Duke and Duchess of Sussex's relationship with the monarchy hit a new low following damaging claims made in the six-part Harry & Meghan show that shed light on their life in California and travails with his family, including Meghan's suicidal thoughts.
Their new project, which will also appear on the streaming service, will be first shown on December 31 and a promotional trailer features footage of Mandela, a human rights stalwart and former president of South Africa, and climate change activist Greta Thunberg.
In the short preview the prince says: “This was inspired by Nelson Mandela who once said ‘what counts in life is not the mere fact that we have lived …'”
The duchess completes the quotation saying “…it is what difference we have made to the lives of others that will determine the significance of the life we lead'”.
The trailer features footage of Mr Mandela shaking hands with children, as well as his "long walk to freedom" when he was released from prison.
The Nelson Mandela Foundation tweeted that it was proud to announce the launch of the series.
Last week, Prince Harry claimed he was shocked when his brother, Prince William, screamed at him during discussions about their intention to move to Canada.
It was reported on Sunday that the couple, who now live in the US, were seeking an apology from the royal family for the unfair way they believe they were treated.
The Sunday Times said the couple felt than an apology by Buckingham Palace aide Lady Susan Hussey to black charity worker Ngozi Fulani meant they deserved equal treatment. Lady Susan had repeatedly asked Ms Fulani "where are you really from" during an event at the palace.
However, despite the rift, there is speculation they will still be invited to King Charles’s coronation on May 6 despite the damaging claims they levelled at the royal family.