With its tunable band-gap and its unique optical and electronic properties black phosphorus (BP) opens exciting opportunities for optoelectronic nanotechnology. The band-gap extends from the visible to the mid-infrared spectral range, as a function of sample thickness and external parameters such as electric field and pressure. This, combined with the saturable absorption and in-plane anisotropic optical properties, makes BP a versatile platform for realizing polarization-sensitive photodetectors and absorbers. Although its near-equilibrium properties have been intensively studied, the development of efficient ultrafast optical devices requires detailed knowledge of the temporal dynamics of the photoexcited hot-carriers. Here we address the electronic response of BP to an ultrafast laser excitation, by means of time-and angle-resolved photoelectron spectroscopy. Following the optical excitation, we directly observe a shift of the valence band (VB) position, indicative of band-gap renormalization (BGR). Our data also show that the hole population in the VB relaxes with a characteristic time tau(VB) = 10.2 +/- 1.0 ps, while the lifetime of the electrons accumulated at the minimum of the conduction band is tau(CB) = 1.9 +/- 0.2 ps. The experimental results are well reproduced by ab initio calculations of the out-of-equilibrium electronic properties. Our study sets the reference for the ultrafast carrier dynamics in BP and demonstrates the material's ultrafast BGR, which is promising for optoelectronic switches.