The former "Glee" star replied: "Yes!!!! Congratulations!! [love heart and stars emojis]."
Busy, 41, was similarly enthusiastic in her response to Hilary's announcement.
She wrote: "Woo!!! Congratulations mama!"
Duff gave birth to her first child when she was 24 and she initially found the experience to be quite "isolating".
However, she also admitted she'd always dreamed of having children.
"I'd say it was a little isolating in the beginning because I didn't have any friends that had babies yet. But I had been working for such a long time that it felt like a natural step for me and I always knew I wanted to be a mom.
"I always knew that was going to be my number one priority in life. So I felt ready on some fronts and a little scared on others, but I really only got scared once I was pregnant."
Hilary has always been open about her experience of pregnancy and although she admits motherhood is challenging, she also relishes it.
She said: "It's just this is what it is. It's messy and it's the best messiest thing ever."
