The 22-year-old said the little boy is expected on April 24.
Peaches, the daughter of Paula and Bob Geldof, also revealed she kept her pregnancy a secret for almost five months, only telling her dad on Boxing Day.
Speaking to Hello! magazine, Peaches said the news that her baby was due on her mum's birthday was "very emotional and touching" and made her think her mother was watching over her. Paula died of an accidental heroin overdose in 2000, when Peaches was just 11.
Peaches says her dad is "just so happy" for her and boyfriend, musician Thomas Cohen, 20:
"I knew he would be happy but I didn't realise how over the moon he would be. He's always been very supportive of me but he was really overwhelmed and emotional."
She said Bob, 60, also approves of her new boyfriend, and prefers him to all her exes: "He offered Tom a glass of champagne and told me he was glad it was Tom because, of all the boyfriends I've had, he's the favourite. He told us we must never break up; that we must make our child happy, get married and be together forever."
The couple got engaged last month after dating for a year. They now plan to bring their wedding forward.
Peaches was previously married to rocker Max Drummey, who she tied the knot with in 2009 in a drive-in Las Vegas ceremony after a 10-day romance. They divorced after six months.
The full interview appears in this week's Hello! magazine, out now.