Lancaster accepted Stewart's marriage proposal in March

Their first child was born at a London hospital weighing 7lbs 7oz.

In a statement, Stewart, 60, said he was "so very proud of my girl Pen" and said the pair could not take their eyes off the new baby.

Lancaster, 34, and Stewart, who have been together for nearly six years, have returned to their home in Epping, Essex, with their son.

The baby was born early on Sunday morning.

"Both Penny and our baby son are gorgeous, healthy and doing well," Stewart said in his statement.

"I am so very proud of my girl Pen for the commitment, courage and strength she showed throughout."

Both Penny and our baby son are gorgeous, healthy and doing well Rod Stewart

"We are celebrating every moment with our beautiful boy, we just can't take our eyes off of him," Stewart said.

Lancaster, meanwhile, described the birth as "the most empowering and spiritual experience of my life."

"It means so much to Rod and I that we were able to keep to our birthing plan and have our baby naturally," she added.

The couple are expected to marry after Lancaster accepted Stewart's marriage proposal at the top of the Eiffel Tower in March.

Before the birth, the star described himself as a father of five children - Kimberley, 25, and Sean, 24, by first wife Alana Stewart; Ruby, 17, by former girlfriend Kelly Emberg; and Renee, 13, and Liam, 10, by second wife Rachel Hunter.

He also has a sixth child, Sarah Thubron, 41, born before he was famous following a teenage romance with art student Susannah Boffey.