When asked about his son as he arrived for the service, William said the family were "in good form, luckily".
Prime Minister Theresa May led the messages of support saying: "My warmest congratulations to the Duke and Duchess of Cambridge on the birth of their baby boy". Prince William replied with a smile: "Jerry's a strong name".
She resumed royal duties just five weeks after giving birth to Prince George, but took four months to appear in public just after the birth of second child, Princess Charlotte. "It is a great joy to have another grandchild, the only trouble is I don't know how I am going to keep up with them", Charles joked in the statement.More news: Jan Oblak casts doubt on Atletico Madrid future
More news: Record-breaking Manchester City keep foot on accelerator
More news: Dow Jones falls almost 425 points; Caterpillar reports earnings plateau
"It is safe, the key thing is support and follow up", ABC News Chief Health and Medical Correspondent Dr. Jennifer Ashton, the author of "Eat This, Not That, When You're Expecting", told Inside Edition.
The newborn son of Prince William, Duke of Cambridge and Catherine, Duchess of Cambridge as they depart the Lindo Wing at St Mary's Hospital on April 23, 2018 in London, England. He also bumps up uncle Prince Harry from fifth to the sixth position in the line to the crown.
The changes in the rules of succession make Princess Charlotte the first royal girl to welcome a baby brother and not lose her line in succession. He is also Queen Elizabeth II's sixth great-grandchild.
Kensington Palace said the baby's name would be announced "in due course".
Charlotte gave a wave to the assembled well-wishers and media as she entered the hospital after William had collected the siblings from school.