Alexis Kawczynski was born at 8.12pm on Saturday at the Royal Shrewsbury Hospital and weighed 8lbs 9oz.
Shrewsbury & Atcham MP Mr Kawczynski, 34, today said he was "thrilled" and thanked all the staff at the hospital who helped his wife Kate, 33, through the birth of their first child.
Mum and baby were still in hospital today and are expected to go home tomorrow.
The Tory MP said Alexis was named in honour of his grandmother, Alexandra.
"Since Saturday I've spent most of my time on the telephone to friends and family and it's all very exciting," he said.
"I gave the baby her first bath and I've changed her nappy already. I'm going to be a very hands-on father.
"I was there at the birth too which was an incredible experience. I'm just thrilled really. It changes your life and makes you far more responsible.
"I have been getting the nursery ready at the house in Shawbury and they will be in hospital until tomorrow morning when they will come home."
Mr Kawczynski paid tribute to the midwives at the RSH saying Kate and Alexis had received "marvellous" care.
"I am so proud she is a Shrewsbury girl," he added.