  The detection of starlight from the host galaxies of quasars during the
reionization epoch ($z>6$) has been elusive, even with deep HST observations.
The current highest redshift quasar host detected, at $z=4.5$, required the
magnifying effect of a foreground lensing galaxy. Low-luminosity quasars from
the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) mitigate the challenge
of detecting their underlying, previously-undetected host galaxies. Here we
report rest-frame optical images and spectroscopy of two HSC-SSP quasars at
$z>6$ with JWST. Using NIRCam imaging at 3.6$\mu$m and 1.5$\mu$m and
subtracting the light from the unresolved quasars, we find that the host
galaxies are massive (stellar masses of $13\times$ and $3.4\times$ $10^{10}$
M$_{\odot}$, respectively), compact, and disk-like. NIRSpec medium-resolution
spectroscopy shows stellar absorption lines in the more massive quasar,
confirming the detection of the host. Velocity-broadened gas in the vicinity of
these quasars enables measurements of their black hole masses ($1.4\times 10^9$
and $2.0\times$ $10^{8}$ M$_{\odot}$, respectively). Their location in the
black hole mass - stellar mass plane is consistent with the distribution at low
redshift, suggesting that the relation between black holes and their host
galaxies was already in place less than a billion years after the Big Bang.
