  During the epoch of reionization (EoR), the 21-cm signal allows direct
observation of the neutral hydrogen (\hi{}) in the intergalactic medium (IGM).
In the post-reionization era, this signal instead probes \hi{} in galaxies,
which traces the dark matter density distribution. With new numerical
simulations, we investigated the end stages of reionization to elucidate the
transition of our Universe into the post-reionization era. Our models are
consistent with the latest high-redshift measurements, including ultraviolet
(UV) luminosity functions. Notably, these models consistently reproduced the
evolution of the UV photon background, which is constrained from Lyman-$\alpha$
absorption spectra. We studied the dependence of this background on the nature
of photon sinks in the IGM, requiring mean free path of UV photons to be
$\sim$10 comoving-megaparsecs (cMpc) during the EoR that increases gradually
with time during late stages ($z\lesssim 6$). Our models revealed that the
reionization of the IGM transitioned from an \textit{inside-out} to an
\textit{outside-in} process when the Universe is less than 0.01 per cent
neutral. During this epoch, the 21-cm signal also shifted from probing
predominantly the \hi{} in the IGM to that in galaxies. Furthermore, we
identified a statistically significant number of large neutral islands (with
sizes up to 40 cMpc) persisting until very late stages ($5 \lesssim z \lesssim
6$) that can imprint features in Lyman-$\alpha$ absorption spectra and also
produce a knee-like feature in the 21-cm power spectrum.
