  We report on the discovery by the Nuclear Spectroscopic Telescope Array
(NuSTAR) and the Neutron Star Interior Composition Explorer (NICER) of the
accreting millisecond X-ray pulsar IGR J17591-2342, detecting coherent X-ray
pulsations around 527.4 Hz (1.9 ms) with a clear Doppler modulation. This
implies an orbital period of ~8.8 hours and a projected semi-major axis of
~1.23 lt-s. From the binary mass function, we estimate a minimum companion mass
of 0.42 solar masses, obtained assuming a neutron star mass of 1.4 solar masses
and an inclination angle lower than 60 degrees, as suggested by the absence of
eclipses or dips in the light-curve of the source. The broad-band energy
spectrum is dominated by Comptonisation of soft thermal seed photons with a
temperature of ~0.7 keV by electrons heated to 21 keV. We also detect
black-body-like thermal direct emission compatible with an emission region of a
few kilometers and temperature compatible with the seed source of
Comptonisation. A weak Gaussian line centered on the iron K-alpha; complex can
be interpreted as a signature of disc reflection. A similar spectrum
characterises the NICER spectra, measured during the outburst fading.
