  We use neutron spectroscopy to determine the nature of the magnetic
excitations in superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_{c}=20$ K).
Above $T_{c}$ the excitations are gapless and centered at the commensurate
antiferromagnetic wave vector of the parent compound, while the intensity
exhibits a sinusoidal modulation along the c-axis. As the superconducting state
is entered a spin gap gradually opens, whose magnitude tracks the
$T$-dependence of the superconducting gap observed by angle resolved
photoemission. Both the spin gap and magnetic resonance energies are
temperature \textit{and} wave vector dependent, but their ratio is the same
within uncertainties. These results suggest that the spin resonance is a
singlet-triplet excitation related to electron pairing and superconductivity.
