The royal couple moved to California this year shortly before officially stepping down as senior royals in March. Since then, they have lived in a £13 million mansion owned by actor Tyler Perry in the Californian city of Los Angeles.
Recently, the couple purchased their own home around 100 miles from the city.
Royal fans have said the property appears to be perfect for a young family, speculating there could soon be a fourth member of the household.
One social media user said: “That house is just perfect for one or two more kids. Harry and Meghan, please agree.”
Another said: “Good for them! Gorgeous area, I’m sure they will be happy there.”
Regarding children, the Duke stated in a past interview with primate scientist Jade Goodall that he would only like to have “two, maximum!”
Based in Montecito, Santa Barbara, the new nine-bedroom home has been referred to as “The Chateau.”
Page Six reports the house also has 16 bathrooms, a swimming pool, tennis courts and more.
It adds the property also has child-friendly features such as a children’s play house, while photos appear to show play equipment.
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However, a statement issued by the Sussexes’ website reads: “Frogmore Cottage will continue to be the property of Her Majesty the Queen.”
As spokesperson for the Sussexes has confirmed the move, saying they moved in in July and adding Meghan and Harry “have settled into the quiet privacy of their community since their arrival.”
The up-market community is home to other celebrities including US television personality Oprah Winfrey.
It is one the richest areas in the United States, with some homes worth in excess of $100 million.
Ms Winfrey’s own Santa Barbara home is worth around $90 million.
Royal author Omid Scobie, who co-wrote a recent biography of the couple – Finding Freedom – called the property “a peaceful home.”
He added: “It has space for Archie, a playground. Really, it’s gonna be a special part of their life.”
In June, Meghan and Harry signed up with the high-profile Harry Walker Agency, which hires out public speakers.
It is claimed the couple could charge up to $1 million per speech at the agency