Branches of cosmic inflationary models, such as slow-roll inflation, predict a background of primordial gravitational waves that imprints a unique odd-parity "B-mode" pattern in the Cosmic Microwave Background (CMB) at amplitudes that are within experimental reach. The BICEP/Keck (BK) experiment targets this primordial signature, the amplitude of which is parameterized by the tensor-to-scalar ratio r, by observing the polarized microwave sky through the exceptionally clean and stable atmosphere at the South Pole. B-mode measurements require an instrument with exquisite sensitivity, tight control of systematics, and wide frequency coverage to disentangle the primordial signal from the Galactic foregrounds. BICEP Array represents the most recent stage of the BK program, and comprises four BICEP3-class receivers observing at 30/40, 95, 150 and 220/270 GHz. The 30/40 GHz receiver will be deployed at the South Pole during the 2019/2020 austral summer. After 3 full years of observations with 30,000+ detectors, BICEP Array will measure primordial gravitational waves to a precision σ (r) between 0.002 and 0.004, depending on foreground complexity and the degree of lensing removal. In this paper we give an overview of the instrument, highlighting the design features in terms of cryogenics, magnetic shielding, detectors and readout architecture as well as reporting on the integration and tests that are ongoing with the first receiver at 30/40 GHz.