Following an eight year struggle with IVF, the radio host, 53, and his partner Amelia welcomed their first child on Friday.
The tot was born a month premature and the host revealed that he rushed to be by his wife's side.
He told talkRADIO: "I think babies are generally really ugly, but mine, mine is beautiful. I've said it.
"She cried which is good, and because she's premature she has to feed every three hours.
"Luckily, Amelia is still in hospital which means I don't have to do any of it."
The presenter added: "It's all very, very strange I have to say. Amelia is doing good – she suffered pre-eclampsia which is why I had to rush from the studio on Friday."
Cassady weighed in at five and a half pounds, and Amelia is still in hospital with the little one.
Speaking about the inspiration behind the baby's name, Matthew said: "It has nothing to do with David Cassady. Neal Cassady is the inspiration, otherwise known as Dean Moriarty.
"If you're a fan of Jack Kerouac's famous beat novel On the Road, Neil Cassady is the anti-hero, he's the loser that everybody loves.
"It's an Irish name, Irish descent with the a, means curly hair. Which Amelia underneath her straightened hair beats a curly vixen."
The couple had tried to have kids several times after Amelia had an ectopic pregnancy in 2009 having fallen pregnant with twins, which Matthew previously said had nearly killed her.
He revealed on Friday that he had been sent a text from his other half that they would having the baby – but only after he had finished his TalkRADIO show.
She messaged him saying: “Ok we are having a baby this evening or basically as soon as you get here. you will be taken to the labour ward and given blue pyjamas to wear. Xx”
The former presenter of Channel 5’s The Wright Stuff previously told The Sun Online he was embracing the prospect of fatherhood, despite always being honest about never wanting children.
Amelia announced the pregnancy on Twitter last September, writing: "After eight challenging years of IVF, we are thrilled to announce that on our last roll of the dice, we got lucky and are expecting a baby girl. Woo hoo! @Matthew_Wright."
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