Firefighters in breathing apparatus entered the mid-terrace house in Collingwood Road, Sutton, on Thursday evening, as it was being ravaged by an "intense blaze", before removing each of the four children and giving them CPR.
London Fire Commissioner Andy Roe said their deaths had "left everyone numb with profound sadness".
The fire was under control by 8.36pm and the cause is under investigation.
Mr Roe said: "This is an incident that has left everyone numb with profound sadness. My thoughts are with the family and friends of the children, the whole local community and all those who will be affected by this fire.
"Fire crews arrived quickly and located the children inside the property.
"They were brought out of the house and given immediate emergency care.
"The welfare of our staff involved in this incident is very important to us and all of them will be offered counselling as a priority."
The London Fire Brigade said eight fire engines and around 60 firefighters were called to the scene at just before 7pm.
The Metropolitan Police said no arrests have been made, but road closures were in place.
It said the children's next of kin are aware and will be provided with specialist support.
Superintendent Rob Shepherd said: "The thoughts of everyone at the South Area Command Unit are with the family and friends of these four young children, who have suffered such a devastating and tragic loss tonight.
"I know these sentiments will be shared by the local community, Sutton and London as a whole.
"We remain on scene with our emergency service colleagues and will be working through the night and beyond. At this very early stage the cause of the fire is unknown and will be investigated."
Graham Norton, assistant director of operations at London Ambulance Service, said: "We sent a number of resources to the scene including ambulance crews, advanced paramedics, paramedics in fast response cars, incident response officers and members of our Hazardous Area Response Team (HART).
"We also dispatched trauma teams from London's Air Ambulance and Air Ambulance Kent Surrey Sussex - both teams consisted of a paramedic and a doctor in a car.
"We treated four children at the scene and took them to hospital.
"Our thoughts are with the family and friends of the four young children and everyone affected by this devastating tragedy. "