Eleanor Grace who has been given Les's real surname Heseltine was born at 4.30am at a London hospital.
'We're really thrilled,' Les tell the Daily Mirror. 'This is a dream come true. We're ecstatic!'
Les met Claire, 37, at a charity ball in 2006. It's their first child together.
A spokeswoman for the pair said: 'Mother and baby are both fine.'
Les, 53 who is divorced from Britain's Got Talent star Amanda Holden, 37 also has a son Philip, 28, with his first wife Lynne.
Where to next?
- A new baby, the first few days
- Step families and single parent families
- Your 9-of-the-best baby pics