Jessica Simpson and fiancé Eric Johnson say becoming parents has been ''the greatest experience'' of their lives.

Jessica gave birth to a 9lb 18 oz baby girl this morning (01.05.12), who they named Maxwell Drew Johnson, and the couple are overcome with joy.

A posting on Jessica's website read: ''Eric and I are elated to announce the birth of our baby girl, Maxwell Drew Johnson.

''We are so grateful for all the love, support and prayers we have received. This is been the greatest experience of our lives.''

Although Jessica previously claimed she wanted to give birth in leopard-print, it is unclear if she fulfilled her wish.

She wrote on twitter last week: ''I just woke up from a dream that I wore a leopard caftan in the hospital. Fabulous!! Now I need to find one!(sic)''

Jessica reportedly wanted to have a caesarean birth because she was nervous about how painful it might be.

A source said: ''The thought of giving birth scared the bejeezus out of her. She was so anxious, she was even breaking into cold sweats at night.

''Jessica has no tolerance for pain. She even turned to hypnotherapy to calm her fears about it, but nothing was working.

''She desperately wanted to experience the joy of a natural birth, but decided to go with what made the most sense for her.''