Tumour-agnostic drugs do not care where the cancer is growing in the body as long as it has a specific genetic abnormality inside.
UK doctors testing the drugs said they were "a really exciting thing".
They said the approach had the potential to cure more patients and cut side-effects.
The drug that has been approved is called larotrectinib.
Charlotte Stevenson, a two-year-old from Belfast, was one of the first patients to benefit.
She was diagnosed with infantile fibrosarcoma, a cancer of the body's connective tissue.
She has been treated with larotrectinib as part of a clinical trial at the Royal Marsden Sutton, in London, for the past year.
Her mum, Esther, said: "We knew that our options were limited [so] we decided to give it a try and are so glad that we did. BBC.