The pair named the girl Lilibet Diana Mountbatten-Windsor, Lili for short.
The name has nods to Queen Elizabeth and the late Princess Diana.
CNN's Royal correspondent Victoria Arbiter told Tim Beveridge the couple managed to keep the birth under wraps for a while.
"When we think about the fact that this news didn't break until today, it's quite remarkable that Harry and Meghan were able to keep this secret.
"Living in California, no doubt they have been under surveillance from paparazzi outlets."
She says this is cause for celebration.
"Here we are, a couple of months since Prince Philip died.
"We've had horrible royal news this year between rifts and Oprah interviews and everything else."
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