To elucidate the magnetic structure and the origin of the nematicity in FeSe, we perform a high-pressure ^{77}Se NMR study on FeSe single crystals. We find a suppression of the structural transition temperature with pressure up to about 2 GPa from the anisotropy of the Knight shift. Above 2 GPa, a stripe-order antiferromagnetism that breaks the spatial fourfold rotational symmetry is determined by the NMR spectra under different field orientations and with temperatures down to 50 mK. The magnetic phase transition is revealed to be first-order type, implying the existence of a concomitant structural transition via a spin-lattice coupling. Stripe-type spin fluctuations are observed at high temperatures, and remain strong with pressure. These results provide clear evidence for strong coupling between nematicity and magnetism in FeSe, and therefore support a universal scenario of magnetic driven nematicity in iron-based superconductors.