  We transform the metric of an isolated matter source in the multipolar
post-Minkowskian approximation from harmonic (de Donder) coordinates to
radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU
metric as a functional of the mass and current multipole moments of the source,
valid all-over the exterior region of the source. Imposing appropriate boundary
conditions we recover the generalized Bondi-van der Burg-Metzner-Sachs residual
symmetry group. To quadratic order, in the case of the mass-quadrupole
interaction, we determine the contributions of gravitational-wave tails in the
NU metric, and prove that the expansion of the metric in terms of the radius is
regular to all orders. The mass and angular momentum aspects, as well as the
Bondi shear, are read off from the metric. They are given by the radiative
quadrupole moment including the tail terms.
