The film director shared the wonderful news with an emotional message on Twitter.
Alongside a cartoon image he wrote, "1 month since dad died today. Made this card for him at Christmas. Due in June. Circle of life. Love you, granddad."
David Bowie passed away on January 10 following a private 18-month battle with cancer.
Duncan was born as Zowie Bowie and is the singer's eldest child - his mother is Angie from whom he's been estranged for around three decades. Angie was in the Celebrity Big Brother House in the UK when the tragic news broke of David's death.
Meanwhile 44-year-old Duncan married his long-time girlfriend Rodene Ronquillo, a photographer, in November 2012. In a sad turn of events, Rodene was diagnosed with breast cancer on the very same day.
The 35-year-old underwent chemotherapy and a double mastectomy and was given the all-clear 11 months later.
The mum-to-be joked on social media, "Shame on those of you who just thought I was really fat and didn't say anything. HAHA ;)"
This will be the first child for both Duncan and Rodene.
Meanwhile, David's widow Iman marked the one-month since his passing with a quote by Rune Lazuli.
"Each tear is a poet, a healer, a teacher."