A geometrically exact spatial beam finite element for thin-walled web- and flange-tapered I-section members is presented. The element is derived from the 3D continuum, by applying standard simplifying assumptions of thin-walled beam theory, but is otherwise geometrically exact. In particular, the torsion-related warping function derived is fully consistent with the tapered geometry. The element can capture load eccentricity effects (loads offset from the centroid-shear center) and Wagner effects. All expressions required to implement the proposed two-node finite element are provided in a simple matrix-vector format. Several numerical tests are presented and discussed, to show the accuracy and computational efficiency of the proposed element in both linear, linear stability (calculation of bifurcation loads and buckling modes) and large displacement path-following analyses. A comparison is made with results taken from the literature or obtained with refined shell finite element models, and in all cases it is concluded that the proposed element is extremely accurate.