Lady Susan Hussey met the head of the Ngozi Fulani charity to apologize after repeatedly asking "where she was really from" at an event last month.
Mrs. Hussey, 83, resigned from role as royal attendant after questioning Ms Fulani's background during a reception a Buckingham palace.
On Friday, Buckingham Palace described the couple's meeting as "full of warmth and understanding" and that Lady Hussey had offered her "sincere apologies".
The statement added: "Lady Susan is committed to deepening her awareness of the sensitivities involved and is grateful for the opportunity to learn more about the issues in this area.
โMs. Fulani, who has been wronged by the most appalling torrent of abuse on social media and elsewhere, has accepted this apology and appreciates that there was no malice.
โThe Royal Houses will continue to focus on inclusion and diversity, with an enhanced work program that will scale up training and awareness programmes, examining what can be learned from Sistah Space and ensuring these reach all members of their communities.
โBoth Ms Fulani and Lady Susan are now asking to be left alone to rebuild their lives after an immensely harrowing period for both of them.
โThey hope their example shows that a path can be found to resolve with kindness, cooperation and condemnation of discrimination wherever it takes root.
โIt is the wish of both parties that, at the end of the 16 days of UN Gender-Based Violence Activism, the focus can now return to the important work of Sistah Space to support women affected by domestic abuse.โ
Buckingham Palace also went on to say that the Queen Consort and the King "were upset that both parties had reached this result."
Lady Hussey, had been a close confidant of the Queen and accompanied her to Prince Philip's funeral. She met the head of the Sistah Space charity along with 300 guests at the palace for an event on domestic and sexual abuse of women.
At the event, Ms Fulani said Lady Hussey pushed her hair back to see her nameplate before asking questions about her family's heritage. After Ms Fulani revealed the incident, both Lady Hussey and Buckingham Palace apologized.
