Sheeran revealed in the Instagram post that Seaborn gave birth last week, adding that both she and their daughter are 'doing amazing'.
Sharing a photo of a baby blanket and socks on Instagram, the singer wrote: "Ello! A quick message from me as I have some personal news that I wanted to share with you... Last week, with the help of an amazing delivery team, Cherry gave birth to our beautiful and healthy daughter - Lyra Antarctica Seaborn Sheeran.
"We are completely in love with her. Both mum and baby are doing amazing and we are on cloud nine over here. We hope that you can respect our privacy at this time. Lots of love and I'll see you when it's time to come back."
Sheeran and Seaborn remain fairly private about their personal life together, having kept fans guessing about their official status after marrying in secret.
They announced their engagement back in January 2018, but never publicly confirmed a wedding had taken place, despite various hints that they had tied the knot.
Last summer, however, Sheeran subtly mentioned their nuptials during an interview with iHeartRadio, when he was asked about the lyrics of 'Remember the Name', specifically the verse that says: "Watch how the lyrics in the songs might get twisted / My wife wears red, but looks better without the lipstick."
Sheeran explained that he'd written the song before he and Seaborn wed, but knew that by the time the song was released they'd be husband and wife.
"It was actually before me and Cherry got married and I knew that we'd be married by the point that the song came out," he said.
"[I thought] Someone's gonna hear that and be like, 'Oh, they're married!' I didn't know how that would be construed, but obviously it's already come out."