  We directly construct model-independent mass profiles of galaxy clusters from
combined weak-lensing distortion and magnification measurements within a
Bayesian statistical framework,which allows for a full parameter-space
extraction of the underlying signal. This method applies to the full range of
radius outside the Einstein radius, and recovers the absolute mass
normalization. We apply our method to deep Subaru imaging of five high-mass
(>10^{15}M_{sun}) clusters, A1689, A1703, A370, Cl0024+17, and RXJ1347-11, to
obtain accurate profiles to beyond the virial radius (r_{vir}). For each
cluster the lens distortion and magnification data are shown to be consistent
with each other, and the total signal-to-noise ratio of the combined
measurements ranges from 13 to 24 per cluster. We form a model-independent mass
profile from stacking the clusters, which is detected at 37{\sigma} out to R ~
1.7r_{vir}. The projected logarithmic slope steepens from -1.01 \pm 0.09 at R ~
0.1r_{vir} to -1.92 \pm 0.51 at R ~ 0.9r_{vir}. We also derive for each cluster
inner strong-lensing based mass profiles from deep HST/ACS observations, which
we show overlap well with the outer Subaru-based profiles and together are well
described by a generalized form of the Navarro-Frenk-White profile, except for
the ongoing merger RXJ1347-11, with modest variations in the central cusp slope
(-dln{\rho}/dlnr < 0.9). The improvement here from adding the magnification
measurements is significant, ~30% in terms of cluster mass profile
measurements, compared with the lensing distortion signal.
