The new parents have named their son Bingham.
Proud dad Matt took to (where else?) Twitter to announce the name, posting the very sweet message:
'So happy! Just had a baby boy, Bingham 'Bing' Hawn Bellamy.
'Mum and baby are strong and healthy. Mum was a warrior, Bing popped out after 4.5 hours of intense pushing!'
A little while later the Muse frontman returned to Twitter with more info on the name choice, tweeting:
'For those wondering, Bingham is my mum's maiden name. Bing Russell was also Kurt [Russell's] dad. Family connections all around!'
Bingham is the couple's first baby together, but Kate has a seven-year-old son, Ryder, with her ex-husband, Chris Robinson.
What do you think of their name choice?