We report and demonstrate a high-resolution extrinsic Fabry-Perot interferometer (EFPI)-based 2-D fiber optic inclinometer for tilt measurements in two orthogonal dimensions. The inclinometer consists of a pair of perpendicularly arranged EFPI sensors packaged inside a rectangular container box. A triangular-shaped metal prism is attached to the top plate of the container box by three ropes with identical lengths. Two optical fibers are rigidly connected to the top plate of the container box by two supporting rods, respectively. Therefore, two EFPI sensors are formed between the endfaces of two optical fibers and their corresponding side face mirrors. The prism is connected to a cross paddle, which is immersed in a damping fluid to reduce the influence of deleterious vibrations. After tilting, the two reflectors of each EFPI sensor will remain parallel, while the cavity lengths of the EFPI sensors change. Changes in the cavity lengths can be calculated, and the 2-D tilt angles of the inclinometer can be calculated according to the Fabry-Perot principle. The design of the sensor and the measurement principles are discussed. Measurements of the tilt angles of a simply supported beam induced by small loads are presented to verify the tip-angle resolution and uncertainty of the two EFPI sensors in our 2-D inclinometer. The results show the capability for metering tilt angles with high resolution. The 2-D inclinometer was used to continuously monitor the tilt angle of a gravity dam for a one-year period, showing excellent stability and practicability.