Prozac can be prescribed for children as young as eight, the European Medicines Agency has said.
Prozac is one antidepressant which is recommended for under-18s
It decided the benefits outweighed the risks in children with moderate to severe depression who failed to respond to psychological therapy.
However, it ruled the drug should only be used in combination with on-going therapy.
Mental health campaigners said it was vital that any use of the drug in children was closely monitored.
Prozac, or fluoxetine, was developed by Eli Lilly and Co but is now widely available in generic versions.
It is one of a class of drugs known as Selective Serotonin Reuptake Inhibitors (SSRIs).
There is evidence suggesting that some SSRIs are associated with an increased risk of suicidal behaviour and thoughts.
Following a review the UK regulator, the Medicines and Healthcare products Regulatory Agency, ruled that most SSRIs were not suitable for use in adolescents.
However, it decided that the benefits of Prozac alone outweighed the risks, and so ruled that the drug could be given to under-18s.
In its latest ruling, the EMEA's Committee for Medicinal Products for Human Use (CHMP) said children should be started on a 10mg daily dose of Prozac.
This could be increased to 20mg per day after one to two weeks.
But if no clinical benefit is seen within nine weeks, treatment should be reconsidered.
A system will be put in place to obtain safety data on use of the drug in children, in particular whether there is any impact on sexual development.
CHMP also stressed that doctors and parents should carefully monitor children and adolescents for suicidal behaviour, particularly at the beginning of treatment.
Paul Farmer, chief executive of the mental health charity Mind, highlighted problems concerning another SSRI, Seroxat.
The drug was Britain's best-selling anti-depressant, but has been found to induce aggressive and suicidal feelings in children and adults.
He said: "It's vital that the lessons from Seroxat are learned.
"Clinicians must exercise extreme caution in administering this treatment to children and adolescents, including very careful monitoring of reactions in this group.
"We would encourage doctors, patients and carers to make full use of the Yellow Card reporting scheme to ensure data on adverse drug reactions is adequately captured by the drugs regulation agencies."
The charity YoungMinds welcomed the EMEA decision.
Avis Johns, the charity's development director, said: "The impact of severe depression on the child, their family and wider community can be devastating.
"Though quite rare, the ability to combine a range of therapies with appropriate medication can provide significant benefits and should therefore be welcomed."
It is estimated that one in ten children are affected by mental illness.