"Emily's fantastic," Peter told Scott Mills on BBC Radio 1. "She's great. She's feeling good and the baby's beautiful."
The television personality, 40, seems to be settling well into his country life in Somerset and described his daily routine of bonding with little Amelia.
"I get up in the morning, I take Amelia downstairs and grab my coffee," said Peter. "And then we go around and talk to the fish, we feed the chickens and we go outside and collect the eggs."
Peter admitted that he was still adjusting to the baby's new name — which took almost a month to choose. The doting father-of-three added that the family had started off by calling Amelia "baby" and then tried out "Rose," but it didn't fit.
The important decision of naming the adorable tot couldn't be made without Peter's two children from his previous marriage, Junior and Princess.
"We both sat around with Junior and Princess and decided on the name, hands up, hands down," said Peter. "Three picked Amelia and one picked Isabella."
The Mysterious Girl singer has previously revealed that he and Emily are planning to wed in a "traditional" ceremony.
"We're definitely going to get married," Peter told show hosts John Stapleton and Lorraine Kelly on Daybreak. "I want a traditional English and traditional Greek wedding, and I want to do two separate ones.
"It's going to be a couple of years yet but it will be English and it will be Greek."