"#ItsABoy Please welcome to the world Wilfred Otto Walbyoff (Wilf to his pals)," wrote Natalie on Twitter. "We are besotted! @OwainWalbyoff.
"Step aside @RyanGosling," she added. "There's a new man in my life #ItsABoy."
Proud dad Owain was quick to retweet his wife's post, which included a touching photo of Natalie and smiley newborn Wilfred.
Natalie's older brother Sam sent his congratulations to the couple on Twitter, writing: "Look at that cheeky little monkey, I'm gonna get him in all sorts of trouble!! @OwainWalbyoff @NataliePinkham."
Natalie and Owain have become first-time parents
University of Nottingham graduate Natalie announced her pregnancy to HELLO! in July, telling the magazine she learned she was expecting after 'feeling different' whilst covering the Barcelona Grand Prix in May.
The new arrival comes two-and-a-half years after Natalie and Owain tied the knot in July 2012.
Whilst the couple haven't confirmed their new son's date of birth, they announced the news on 17 January – the same Natalie's close friend Zara Tindall's daughter Mia turns one.
Zara was by Natalie's side when she married Owain in Obidos, Portugal, as was Zara's royal cousin Princess Eugenie.