The two children were savaged by a dog, believed to be a family pet, in a relative’s home in Colchester as their mother tried to fight it off.
In a statement the children’s devastated parents said: “Our beautiful sons Archie Joe Darby and Daniel-Jay Darby are so, so loved by us all and were such happy little loveable boys.
“We have lost our gorgeous little four–month-old baby and our beautiful 22-month-old boy is currently being treated for his injuries.
The children’s mother was also hurt as she desperately fought to stop the attack by the animal.
Both boys were taken to hospital but doctors were unable to save the youngest Archie Joe, who was four-months-old.
The dog involved, said to be a Staffordshire bull terrier, was removed by police and later put down with the consent of the owner.
A post-mortem examination on Archie’s body is expected to take place next week, Essex Police said.
Chief Inspector Elliott Judge said: “This is a tragic incident where a young child has lost his life.
“We can confirm the incident took place inside a house on Harwich Road, the dog has been destroyed, and no-one has been arrested.