We use polarized inelastic neutron scattering to study low-energy spin excitations and their spatial anisotropy in electron-overdoped superconducting BaFe1.85Ni0.15As2 (Tc = 14 K). In the normal state, the imaginary part of the dynamic susceptibility, χ ′′ (Q, ω), at the antiferromagnetic (AF) wave vector Q = (0.5, 0.5, 1) increases linearly with energy for E ≤ 13 meV. Upon entering the superconducting state, a spin gap opens below E ≈ 3 meV and a broad neutron spin resonance appears at E ≈ 7 meV. Our careful neutron polarization analysis reveals that χ ′′ (Q, ω) is isotropic for the in-plane and out-of-plane components in both the normal and superconducting states. A comparison of these results with those of undoped BaFe2As2 and optimally electron-doped BaFe1.9Ni0.1As2 (Tc = 20 K) suggests that the spin anisotropy observed in BaFe1.9Ni0.1As2 is likely due to its proximity to the undoped BaFe2As2. Therefore, the neutron spin resonance is isotropic in the overdoped regime, consistent with a singlet to triplet excitation.