  We derive a compact representation of the renormalized $N$-jettiness soft
function that is free of infrared and collinear divergences through
next-to-next-to-leading order in perturbative QCD. The number of hard partons
$N$ is a parameter in the formula for the finite remainder. Cancellation of all
infrared and collinear singularities between the bare soft function and its
renormalization matrix in color space is demonstrated analytically.
