To avoid the overflow from @Evan Teran 's answer, I'll just use a wider type, ie size_t suitable for common use cases.

convert.cpp

#include <iostream>
#include <sstream>
#include <exception>

size_t convertHex(const std::string& hexStr)
{
    std::cout << "This trick can print values up to: " << static_cast<size_t>(-1);
    std::cout << std::endl;

    std::stringstream ssBuff {};
    size_t x {0};

    ssBuff << std::hex << hexStr;
    ssBuff >> x;

    if(!ssBuff.eof() || ssBuff.fail())
    {
        throw std::runtime_error("Conversion in stringstream failed.");
    }

    return x;
}

int main(int argc, char* argv[])
{
    if(2 != argc)
    {
        std::cout << "Usage: " << argv[0] << "  [hex_string_to_convert].";
        std::cout <<  std::endl;
        return -1;
    }

    try
    {
        std::string hexStr{argv[1]};
        size_t value = convertHex(hexStr);
        std::cout << hexStr << " = " << value << std::endl;
    }
    catch(std::runtime_error &e)
    {
        std::cout << "\tError: " << e.what() << std::endl;
        return -1;
    }

    return 0;
}

g++ -o app convert.cpp && ./app fffefffe

Output:

This trick can print values up to: 18446744073709551615

fffefffe = 4294901758

./app fffefffefffffffffffffffffffffffffffffffff

Output:

This trick can print values up to: 18446744073709551615

Error: Conversion in stringstream failed.