The order followed publication of a landmark review earlier this year into gender care services for children by the paediatrician Dr Hilary Cass.
It found a lack of evidence around treatment for under-18s with puberty-blocking drugs.
In March, NHS England decided that puberty blockers would no longer be routine treatment for children with gender dysphoria.
Then in May, the Conservative government tightened rules on the drugs, introducing an emergency ban on them being prescribed by private and European prescribers.
This was kept in place by Labour when they came to power and was subsequently challenged in the High Court. The government won that case.
Announcing the indefinite ban, Streeting said: “It is a scandal that medicine was given to vulnerable children without the proof that it was safe or effective.”
But Streeting said the planned clinical trial by NHS England into the use of puberty blockers was going ahead.
He said the ban would then be reviewed in 2027 in the light of any new evidence that emerged.
Under-18s who were on the drugs before the ban was introduced have been allowed to continue using them.
