Children's symptoms were generally mild. Some who tested positive had no symptoms, but about one in 10 in the study needed intensive care.
Doctors say the work is "reassuring", but more needs to be known about treatments for the seriously ill.
What did the study find?
Researchers led by a team at London's Great Ormond Street looked at 582 children aged from three days up to 18 years living in 25 European countries.
They all tested positive for Covid-19 during the initial peak of the pandemic in April and had been seen at one of 82 specialist healthcare centres for their symptoms.
A quarter had underlying health conditions.
Of the four deaths during the study (0.69%), none were in children under 10, and two of those who died had pre-existing health conditions.
More than half of the children studied were admitted to hospital, and 8% needed treatment in intensive care.
What symptoms did the children have?
Children commonly had a fever (65%), upper respiratory tract infection (54%), pneumonia (25%) and gastrointestinal symptoms (22%).
Some of the children (16%), most of whom were tested due to close contact with a known case, had no symptoms at all.
Just an extract from a BBC News article but the study is available to see and read online