The couple also took to Instagram to show their support for the growing family after news of the birth broke on Sunday.
"We are all delighted by the happy news of the arrival of baby Lili," they captioned a black and white photo of a then-pregnant Markle, 39, sharing a sweet embrace with Harry, 36, and their firstborn Archie, 2.
"Congratulations to Harry, Meghan and Archie," they added.
The baby girl was born at 11:40 a.m. at the Santa Barbara Cottage Hospital in Santa Barbara, California, and weighed in at 7 lbs, 11 oz, a spokesperson for the couple said. The child is eighth in line to the British throne.
"Thank you for your continued kindness and support during this very special time for our family," the couple wrote in a statement that accompanied the birth announcement.
The baby is "more than we could have ever imagined, and we remain grateful for the love and prayers we’ve felt from across the globe," they continued.
In recent months, the British royal family has been embroiled in tension and drama following Harry and Markle’s explosive interview with Oprah Winfrey in March. Their claims included accusations of racism and turning a blind eye to mental health struggles.
Since then, it’s understood that Harry and William have had conversations that were "not productive," according to Gayle King. However, it seems Middleton is working to remedy that.
"The harsh truth – in my opinion – is that if Harry doesn’t get a grip and stop this self-indulgent episode, there will soon be no common ground or relationship to rebuild," Middleton’s uncle, Gary Goldsmith, told Closer. "But if anyone can bring peace to the royals, Kate can. Kate is a brilliant arbiter and peacemaker."
He added: "Every bone in her body is about making friends and doing the best she can... She’s trying to mediate."
It’s been reported that Middleton put in some work on the brothers’ relationship in April when they reunited for the funeral of their grandfather, Prince Philip, which Goldsmith made note of.
"You could see at the funeral that Kate was there trying to make peace, bringing the brothers together," he said. "Harry and Kate were great friends, they were a trio with William and a strong unit. Family and relationships are everything to Kate – she’s very nurturing, she wouldn’t like that [rift] happening and she is trying to look after her husband and do what she can to make things right."
It seems that the extended family’s feelings about Harry and Markle may be souring, however, as Goldsmith said his own thinking has shifted.
"I went from being happy [about Harry taking the decision to seek a more private life] to angry, to worried about him," he admitted. "Everyone is astonished. He wanted to step back and protect his wife, now he’s charging in. It’s an attack on the family – why do it? If you want an easy life, work it out privately and have a conversation respectfully. Don’t air it in public, it’s really hurtful."
Furthermore, Goldsmith, brother to Middleton’s mother Carole, said that "if Harry doesn’t get a grip and stop this self-indulgent episode, there will soon be no common ground or relationship to rebuild."
The Duke and Duchess of Sussex’s departures from royal duties began last year over what they described as the British media’s intrusions and racist attitudes towards the duchess. The family now resides in the coastal city of Montecito, Calif.
Fox News' Nate Day and The Associated Press contributed to this report.