The Busted singer, 33, and his presenter wife Emma, 40, have called their daughter Trixie Grace.
"They couldn't be more made up and are enjoying precious time together as a family," a source close to the couple told The Sun.
The couple already have a son and daughter
The proud couple are already parents to six-year-old Isabelle and four-year-old Ace. The birth comes just days before new dad-of-three Matt will embark on a Busted UK tour with his fellow bandmates James Bourne and Charlie Simpson.
The singer had previously admitted that he was "cutting it pretty fine" as his wife was due on 4 May. Other reports claim that Emma gave birth on Saturday 7 May, although neither the presenter nor the band member have announced the arrival of their new baby on social media.
Emma gave birth earlier this week
Emma's pregnancy was announced in December, when a source told The Sun: "Emma and Matt are thrilled. It's something they've been talking about for some time. But there will have to be compromises as the baby will come at a time when they're both super busy.
"Emma has major commitments to The Voice and Big Brother, which she'd obviously like to honour, and Matt has been fully focusing on making Busted's comeback go well. They know they'll make it work. They're used to juggling their family with increasingly busy careers."
The couple have named their daughter Trixie Grace
The Voice presenter has made no secret of her desire to have another baby, telling Now magazine that she was trying to convince Matt that it was a good idea.
"I go, 'It'd be nice to have one more'. Then Matt goes, 'We've only just started sleeping'," Emma said. "So he says no but I say, 'But soon we won't have a baby anymore…' I don't know – you don't plan these things."