In this paper, we introduce and demonstrate a novel optical fiber extrinsic Fabry-Perot interferometer (EFPI) for tilt measurements with 20 nrad resolution. Compared with in-line optical fiber inclinometers, an extrinsic sensing structure is used in the inclinometer reported herein. Our design greatly improves on the tilt angle resolution, the temperature stability, and the mechanical robustness of inclinometers with advanced designs. An EFPI cavity, which is formed between endfaces of a suspended rectangular mass block and a fixed optical fiber, is packaged inside a rectangular container box with an oscillation dampening mechanism. Importantly, the two reflectors of the EFPI sensor remain parallel while the cavity length of the EFPI sensor meters a change in tilt. According to the Fabry-Perot principle, the change in the cavity length can be determined, and the tilt angle of the inclinometer can be calculated. The sensor design and the measurement principle are discussed. An experiment based on measuring the tilt angle of a simply-supported 70-cm beam induced by a small load is presented to verify the resolution of our prototype inclinometer. The experimental results demonstrate significantly higher resolution (ca. 20 nrad) compared to commercial devices. The temperature cross-talk of the inclinometer was also investigated in a separate experiment and found to be 0.0041 μrad /°C. Our inclinometer was also employed for monitoring the daily periodic variations in the tilt angle of a windowsill in a cement building caused by local temperature changes during a five-day period. The multi-day study demonstrated excellent stability and practicability for the novel device. The significant inclinometer improvements in differential tilt angle resolution, temperature compensation, and mechanical robustness also provide unique opportunities for investigating spatial-temporal modulations of gravitational fields.