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The 'Smile' singer and husband Sam Cooper welcomed Marnie Rose Cooper on Tuesday (January 8).
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Tweeting this afternoon, Allen confirmed the news by writing: "Quite overwhelmed by all the well wishing going on. THANKYOU everybody x x x."
As if to emphasise her exhaustion, Allen later tweeted: "Tramadol #tramalolz."
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Allen gave birth to her first child with Cooper, Ethel, in November 2011.
The couple married in a 'typical village wedding' in Gloucestershire in June of that year, announcing that Allen was pregnant with Ethel at the reception.
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