23 November 2015 Last updated at 23:09 GMT
She came to the UK as a refugee and was discovered by a modelling scout, despite the fact her dark skin and Dinka features were at odds with the more European look favoured for black models at the time.
Now based in New York, Wek is one of the most recognised fashion models in the world and a passionate campaigner for refugees.
As part of the BBC's 100 Women season she talks to Anne Soy about being a top model, about life as a refugee and about being a unique beauty by western standards. Listen and download the full interview here.
Alek Wek's idyllic childhood was rocked by the civil war in her native southern Sudan.