The Irish model and Made in Chelsea star welcomed their second child last month and already have a son, named Theodore, who was born in September 2018.
Now, two weeks after the birth of their daughter, the couple has confirmed the new arrival’s name: Gigi Margaux Matthews.
Speaking to Hello! magazine about becoming parents for the second time, Matthews said: “Life is just wonderful. There really couldn’t be more love in our house right now.”
Williams opened up about the process of choosing a name, admitting they settled on the moniker “ages ago”.
“When we were discussing names I thought, ‘I want to want her name’, and I do. I just love it. I wish I was called it myself,” she said.
“We decided on it ages ago and as soon as we saw her, we knew it suited her. She is so perfect. I am obsessed with her.”
Spencer added: “I always really liked the name Margaux for a girl, spelt in the French way – like the wine.
“When people ask what she’s called I always say Gigi Margaux – like my dad introduces me as Spencer George sometimes. It rolls off the tongue nicely.”
Williams went on to say that Gigi already has a fully-stocked wardrobe.
“Her wardrobe is already quite extensive,” she joked. “I hope nobody buys me any more baby clothes because we’ve definitely got enough until she’s 18 months. I couldn’t help myself.”
Spencer also commented on how naturally they are adapting to becoming a family of four and said his daughter’s arrival was “a wonderful moment that I’ll treasure”.
“The whole thing was alarmingly unstressful. It felt like I was going out to get a coffee,” he explained.
“Don’t get me wrong, we share all sorts of wonderful moments where we’re just gazing at Gigi adoringly, but it does feel super smooth and straightforward this time.”
The couple announced the birth of their second child on Instagram last month.
Alongside a selfie of them both at hospital, Williams wrote: “Last night we became a family of four. Our beautiful daughter arrived safely and happily into the world.”
Matthews also shared the happy news with his followers on social media, writing: “Wow, we officially have CHILDREN!! So much has happened in the last three years. Real positive change, a son and now a daughter.
“I couldn’t be more thankful to my incredible wife @voguewilliams for all that you do for our family, in particular the laborious pregnancies which us men will never fully understand. I have always dreamt of being a great father and because of you, that is now achievable. Feel lucky every day to be married to you.”
The full interview in Hello! magazine, out now.