She added: "I'll admit I'm not very good at baking, but you have to be the best thing I've ever made! You've absolutely broken your Mum and Dad, we are so in love."
The couple's baby joy comes after Papas penned a moving speech which she read on air when revealing to listeners she was pregnant.
She revealed in October the couple was having a boy, although acknowledging she felt "pretty weird" about gender reveals.
Opening up about the couple's fertility journey last August, she said: "I often say that you should never ask anyone about whether they're having children, or when, or if they're having another, but unless you have ever been on the other side of those questions you don't really understand why it's a big deal."
She added: "We promised ourselves that if we were ever lucky enough to get pregnant, we would be genuine and honest about our journey. People struggle. Please be kind, and although your questions are sweet and innocent, it can be hugely painful for those on the receiving end.
"With that being said, I would like to share the news that Andrew and I are 17 weeks pregnant with our first child - an absolute surprise while we were waiting to start IVF."
On Sunday, Papas shared a sweet Valentine's Day message on Instagram.
"You [Andrew] made my dream of Motherhood come true, and despite the craziness of the past week you still got me flowers. Watching you become the sweetest, loving, and attentive Dad is the best gift you could have given me," she wrote.
Hayley Sproull, comedian and host of TVNZ's Have You Been Paying Attention, is co-hosting with Fletch and Vaughan while Papas is on maternity leave.