She said a new law would be introduced during this session of the Westminster parliament.
Mrs May said it was "scarcely believable" that the problem still existed in the UK.
"Vulnerable people from all over the globe are trafficked into Britain every day," she said. "Most end up working as modern-day slaves, without pay, without rights and without hope."
Stressing that some Britons had been trafficked within the country, Mrs May said whatever the nationality of victims "our first concern must be to free them". She said the best way to do that was to "maximise the number of modern-day slave drivers we convict and imprison".
Since the deaths of 23 Chinese cockle-pickers in Morecambe Bay in 2005, all gangmasters who supply large numbers of workers for agriculture or other labour-intensive activities have been required to be members of the Gangmasters Licensing Authority (GLA).
Mrs May said the Modern Slavery Bill would create trafficking prevention orders, barring anyone convicted of a trafficking offence from gaining GLA membership.
They could also face restrictions on their ability to own a company, visit certain places or work with children or young women.
A modern slavery commissioner will also be appointed to hold law enforcement and government bodies to account.
Mrs May said: "It has been a profound shock to discover the extent to which slavery has reappeared in our country."