Writing to her 340,000 followers on the social media site, Katona wrote: 'Thank you all so much for your kind messages, at last were both home after getting the all clear! It's been very traumatic @mrgsjkay xxxx.'
Kerry and George welcomed a daughter at the weekend
The couple announced on Saturday that Kerry had given birth to a daughter, with Kerry's fiancé George writing: '@KerryKatona7 thank you for bringing my beautiful daughter into this world last night1 You are both amazing xxxxxxxxx'
It's the couple's first child together, although they both have children from previous relationships.
Kerry tweeted last week that she'd stopped being able to see her feet, and that she was struggling to sleep in the latter stages of her pregnancy.