The West Brom prospect has featured for both their under-18s and reserves this season.
A right-sided defender who can also play on the left, he turned 16 in January and is regarded as one of the country's brightest youngsters.
Now the Blues have stepped in to bring Hurst to Fratton Park after he turned down the offer of a new Baggies contract.
West Brom will receive an initial £250,000 compensation fee which will rise to more than £1m depending on performance-related criteria.
It is another coup for director of youth operations Paul Hart as he continues to revolutionise Pompey's youth set-up.