The birth comes days after Barker revealed the couple would call their baby Rocky.
Speaking on an episode of the One Life One Chance with Toby Morse podcast, the Blink-182 drummer said his son’s full name would be Rocky Thirteen Barker.
He is Kardashian’s fourth child after Mason, 13, Penelope, 10 and Reign, eight, who she had with ex-boyfriend and Keeping Up With The Kardashians co-star, Scott Disick.
The couple first revealed their pregnancy when Kardashian recreated a scene from the hit Blink-182 song All The Small Things by holding up a sign at a Blink-182 concert reading: “Travis I’m pregnant.”
They also shared a gender reveal video shortly afterwards, with Kardashian sitting on Barker’s lap at a drum set.
He then began a drum roll before blue streamers and confetti rained down from above.
Last month Kardashian revealed she was recovering from urgent foetal surgery and praised doctors for “saving” her baby’s life.
Kardashian wrote on Instagram: “I will be forever grateful to my incredible doctors for saving our baby’s life.
“I am eternally grateful to my husband who rushed to my side from tour to be with me in the hospital and take care of me afterwards, my rock. And to my mom, thank you for holding my hand through this.
“As someone who has had three really easy pregnancies in the past, I wasn’t prepared for the fear of rushing into urgent foetal surgery.
“I don’t think anyone who hasn’t been through a similar situation can begin to understand that feeling of fear. I have a whole new understanding and respect for the mamas who have had to fight for their babies while pregnant.”
She concluded: “Praise be to God. Walking out of the hospital with my baby boy in my tummy and safe was the truest blessing.”
Barker has two children, Landon, 29, and Alabama, 17, with his ex-wife Shanna Moakler.
The couple held marriage ceremonies in May this year in California and then in Portofino, Italy, after holding a “practice” wedding in Las Vegas a month earlier.
Mr Biden was diagnosed on Friday, with tests revealing the cancer had spread to his bones.
The former president posted an image of himself and his wife Jill on X on Monday and wrote: “Cancer touches us all. Like so many of you, Jill and I have learned that we are strongest in the broken places. Thank you for lifting us up with love and support.”
Image: The King and Joe Biden at Windsor Castle in July 2023. Pic: Reuters
The King’s letter comes after British Prime Minister Sir Keir Starmer said he was “very sorry to hear President Biden has prostate cancer”.
“All the very best to Joe, his wife Jill and their family, and wishing the President swift and successful treatment,” he added.
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Meanwhile US President Donald Trump said he was “saddened” by the news, adding: “We extend our warmest and best wishes to Jill and the family, and we wish Joe a fast and successful recovery.”
Former US president Barack Obama said: “Michelle and I are thinking of the entire Biden family.
“Nobody has done more to find breakthrough treatments for cancer in all its forms than Joe, and I am certain he will fight this challenge with his trademark resolve and grace. We pray for a fast and full recovery.”
Image: Barack Obama (right) with Joe Biden at a campaign event in 2022. File pic: Reuters
After a poor debate performance against Mr Trump and amid escalating concerns around his age and fitness to serve, Mr Biden withdrew from the 2024 presidential election race and endorsed his vice president Kamala Harris.
Ms Harris wrote on X after his diagnosis: “We are keeping him, Dr. Biden, and their entire family in our hearts and prayers during this time.
“Joe is a fighter – and I know he will face this challenge with the same strength, resilience, and optimism that have always defined his life and leadership. We are hopeful for a full and speedy recovery.”
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1:16
Mr Biden’s diagnosis: What we know
Former US president Bill Clinton wrote on social media: “My friend Joe Biden’s always been a fighter. Hillary and I are rooting for him and are keeping him, Jill, and the entire family in our thoughts.”
Hillary Clinton, who unsuccessfully ran for president in 2016, said she was “thinking of the Bidens as they take on cancer, a disease they’ve done so much to try to spare other families from”.
Speaker of the US House of Representatives Mike Johnson said it was “sad news” and his family “will be joining the countless others who are praying” for Mr Biden.
Former House speaker Nancy Pelosi described Mr Biden as a “great American patriot” and said she was “praying for him to have strength and a swift recovery”.
Mr Trump’s secretary of state, Marco Rubio, wrote on social media that he and his wife were “united in prayer for the Biden Family during this difficult time”.
US President Donald Trump said he was “saddened” by the news, adding: “We extend our warmest and best wishes to Jill and the family, and we wish Joe a fast and successful recovery.”
Former US president Barack Obama said: “Michelle and I are thinking of the entire Biden family.
“Nobody has done more to find breakthrough treatments for cancer in all its forms than Joe, and I am certain he will fight this challenge with his trademark resolve and grace. We pray for a fast and full recovery.”
Image: Barack Obama (right) with Joe Biden at a campaign event in 2022. File pic: Reuters
British Prime Minister Sir Keir Starmer said he was “very sorry to hear President Biden has prostate cancer”.
“All the very best to Joe, his wife Jill and their family, and wishing the President swift and successful treatment,” he added.
After a poor debate performance against Mr Trump and amid escalating concerns for his health, Mr Biden withdrew from the 2024 election and endorsed his vice president Kamala Harris.
Ms Harris wrote on X: “We are keeping him, Dr. Biden, and their entire family in our hearts and prayers during this time.
“Joe is a fighter – and I know he will face this challenge with the same strength, resilience, and optimism that have always defined his life and leadership. We are hopeful for a full and speedy recovery.”
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1:16
Mr Biden’s diagnosis: What we know
Former US president Bill Clinton wrote on social media: “My friend Joe Biden’s always been a fighter. Hillary and I are rooting for him and are keeping him, Jill, and the entire family in our thoughts.”
Hillary Clinton, who unsuccessfully ran for president in 2016, said she was “thinking of the Bidens as they take on cancer, a disease they’ve done so much to try to spare other families from”.
Speaker of the US House Of Representatives Mike Johnson said it was “sad news” and his family “will be joining the countless others who are praying” for Mr Biden.
Former House speaker Nancy Pelosi described Mr Biden as a “great American patriot” and said she was “praying for him to have strength and a swift recovery”.
Mr Trump’s secretary of state, Marco Rubio, wrote on social media he and his wife were “united in prayer for the Biden Family during this difficult time”.
Following President Trump’s Middle East trip – which the White House is touting as an unbridled success – Sky News’ Martha Kelner sits down with Barbara Leaf, who was US ambassador to the United Arab Emirates during Trump’s first term and assistant secretary of state for Near Eastern affairs in the Biden administration.
She was also in the team that formed the first formal US presence in Syria after more than a decade.