A source close to Kate added the couple are 'thrilled to bits.'
The newborn is a third child for Kate, but a first for her husband. The baby joins Mia, 13, and Joe, nine, from Kate's first two marriages.
Winslet met Rocknroll while holidaying at his uncle Richard Branson's privately owned Necker Island, where they wed in secret last December after a whirlwind romance.
The 35-year-old works on the space-travel branch of the Virgin empire.
Rocknroll was born Ned Abel Smith, but changed his name to his unusual monkier by deed poll.
Winslet kept her last name on her marriage, telling Usmagazine: 'I was never going to change my name to Rocknroll. I've never changed my name to anything so I didn’t see a reason to start now.'
It is not known which surname the proud parents will give their newborn son, although by referring to 'Baby Boy Winslet' her spokeswoman implied it would be his mother's.
Speaking recently about her pregnancy, Kate told People magazine: 'I feel completely great. Being a parent turns you inside out.
A spokeswoman confirmed the news, saying: “Kate had ‘Baby Boy Winslet’ on Saturday in Sussex. Mother and baby are doing great.”
Kate already has two children - 13-year-old daughter, Mia, with first husband Jim Threapleton and nine-year-old son, Joe, with 'Bond' director, Sam Mendes.