The singer said the couple were on "cloud nine" after their daughter's arrival last week.
Sheeran returned to Instagram for the first time since December to share the news and thank the "amazing delivery team".
He added: "We are completely in love with her."
"Ello! A quick message from me as I have some personal news that I wanted to share with you," Sheeran said in his first Instagram post since December 2019.
"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, Ed x"