According to the newspaper The Sun, his wife, Melia, 29, and the newborn are doing well. The singer was present for the delivery which was at a London hospital.
The couple have two more children together, Julie-Rose, 3 and Ella Mae, 2.
Clapton also has a daughter Ruth, 19, that he shares with his ex-fiancée, Yvonne Kelly.
In 1991, this Eric Clapton tragically lost his four year old son, Conor.