It made the announcement on Friday, less than a week after their televised two-hour tell-all primetime show with Oprah Winfrey was broadcast.
During the programme, Meghan told the chat show host she had been suicidal while in the royal family and claimed she received no help after telling staff about her suffering.
She and Harry also made explosive allegations of racist comments about their one-year-old son, Archie.
In an update from the foundation, it said it would be providing support to Colour of Change, Mind, The PressPad Charitable Foundation and URL Media.
UK-based charity Mind was among those who supported Meghan's openness about her mental health struggles during the interview.
They tweeted: "We applaud Meghan Markle for speaking out about her experiences of suicidal thoughts. We know that opening up in this way can be really difficult, but when high-profile people talk about these experiences, it helps to break down the stigma around mental health issues."
Colour of Change describes itself as the US's "largest online racial justice organisation" and works across criminal justice, voting freedom and economic justice, adding: "We cannot end racism in one area without tackling it in all areas."
The PressPad Charitable Foundation works to improve diversity within the media by "lowering the financial barrier for young people who want to become journalists".
Social enterprise PressPad wrote on Twitter: "We are delighted to announce that we have just registered a sister charity, The PressPad Charitable Foundation, and are thrilled that the Duke and Duchess of Sussex and their Archewell Foundation will be among our first donors.
"We're excited by such positive action after difficult yet important moments of reckoning for the UK media.
"We're proud to say our values of action, compassion & community align with the #archewellfoundation. Thanks to everyone who spoke their truth."
URL Media describes itself as a "multi-platform network of high-performing Black and Brown media organisations" and was launched in January.
On their website, they said: "As the US enters a new chapter, we offer an alternative to business as usual."