For large-span bridge monitoring, displacement measurement is essential. However, it remains challenging to accurately estimate bridge displacement. When displacement is calculated by the double integration of acceleration, a low-frequency drift appears in the estimated displacement. Displacement can also be estimated from strains based on the Euler-Bernoulli beam theory. However, prior knowledge of the mode shapes and the neutral axis location of the target bridge are required for strain-displacement transformation. In this study, we propose a finite impulse response filter-based displacement estimation technique by fusing strain and acceleration measurements. First, the relationship between displacement and strain is established, and the parameter associated with this strain-displacement transformation is estimated from strain and acceleration measurements using a recursive least squares algorithm. Next, the low-frequency displacement estimated from the strain measurements and the high-frequency displacement obtained from an acceleration measurement are combined for high-fidelity displacement estimation. The feasibility of the proposed technique was examined via a series of numerical simulations, a lab-scale experiment, and a field test. The uniqueness of this study lies in the fact that the displacement and the unknown parameter in strain-displacement transformation are estimated simultaneously and the accuracy of displacement estimation is improved in comparison with those of previous data fusion techniques.