The Duchess gave birth to a baby boy at St Mary’s Hospital in West London at 4.24pm yesterday (Monday).
The baby will be third in line to the throne.
In a statement the palace said mother and baby were doing well, and they remained in hospital over night.
Coun Irmgard Parrott said: “I’m delighted and would like to congratulate the Duke and Duchess of Cambridge on the birth of their son.”
“I think they will make wonderful parents and hope they enjoy parenthood. I’m glad both mother and baby are doing well and wish them all the very best.”
“It would be fantastic to see the new prince visit Lincolnshire in the future, and it would be a huge honour to welcome him to West Lindsey especially.”