In the post, which was also shared to Randolph’s Instagram, the 33-year-old wrote: “Welcome to the world our little grape. We already love you more than words can say.”
Burke and goalkeeper Randolph, 34, who plays for West Ham and the Republic of Ireland, revealed they were expecting a child in February when they shared a video to Instagram which showed the pair on a country walk with their two dogs.
In the video, they’re standing near a lake as Randolph gets to his knees to kiss his girlfriend’s stomach.
The clip then showed the couple rubbing Burke’s bump as she smiles.
Since winning The X Factor after duetting with Beyonce, Burke has forged a successful career in music and the West End.
She also appeared on Strictly Come Dancing in 2017, when she was partnered with Gorka Marquez.