The 'Murder On The Dancefloor' singer, 36, gave birth on Tuesday (3 November) and introduced the little tot to her social media followers on Saturday.
Sophie shared an adorable selfie kissing her baby son's head, and the newborn is wrapped up nice and cosy in a blanket.
Behind them in the room, the word 'family' is lit up on the wall.
Sophie also announced the babe's name, writing: "He's here! Baby Jesse Jones, born on Tuesday 3rd November and now home safe with his family. We are all a bit smitten. Welcome to the world, darling boy. Xx."
Many fans shared Sophie's joy, with one replying: "Congratulations!! 4 boys what a blessing. Wishing lots of happiness together."
Another said: "Having 4 boys myself I would advise thermals and wellingtons for the side of a pitch X congratulation lovely X."
On the very day she gave birth, Strictly star Sophie had shown off her enormous bump with her 31.9k Instagram followers.
Alongside a photo of herself in pyjamas, she wrote: "Does my tum look big in this?"
Sophie is married to The Feeling bassist Richard Jones, after a romantic 2005 wedding at Palazzo Terranova in Italy.
Their first son, Sonny, was born in April 2004.
Their second son, Kit Jones, was born in February 2009, followed by Ray Holiday Jones in 2012.
A huge congratulations to Sophie and her family!
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