The couple’s daughter was born by caesarian section at the Royal Cornwall Hospital in Treliske.
David Cameron and Samantha Cameron were on holiday with their family in the area, as the baby was not due until September.
Speaking outside the hospital shortly after the birth, the Prime Minister said he was the “proud dad” of a “beautiful” daughter.
Cameron said his wife woke up in the morning and realised she was having contractions so they went to the hospital before “it all just kicked off a bit quickly”.
“It’s lovely to be here in Truro and have the baby here,” he told reporters.
He joked that they were open to suggestions for what to call their daughter. “We will have to have something Cornish in there somewhere,” he added.
The couple arrived at the NHS hospital at around 8am and their daughter was delivered at approximately midday.
“The Prime Minister and Mrs Cameron are delighted to announce the birth of their fourth child, a baby girl,” a Downing Street spokesman said.
“Both the baby and Mrs Cameron are doing very well.
“The PM and Mrs Cameron would like to thank the doctors and nurses at the hospital for their help and kindness.”
Cameron will take some paternity leave but he is expected to be back at his desk at the end of next week.
The couple also have a daughter, six-year-old Nancy and four-year-old son Arthur Elwen, who is known by his middle name
Their eldest son, Ivan, died in 2009 at the age of six. He had cerebral palsy and severe epilepsy.
The Camerons made no secret of their hopes for another child and the pregnancy was announced shortly before the General Election in May.
Among the first public figures to react to the Camerons’ news were Labour leadership rivals David and Ed Miliband. Sky News