  Nuclear Star Clusters (NSCs) are amongst the densest stellar systems in the
Universe and are found at the centres of many bright spiral and elliptical
galaxies, and up to ${\sim}$40% of dwarf galaxies. However, their formation
mechanisms, and possible links to globular clusters (GCs), remain debated. This
paper uses the EDGE simulations - a collection of zoom-in, cosmological
simulations of isolated dwarf galaxies -- to present a new formation mechanism
for NSCs. We find that, at a gas spatial and mass resolution of ${\sim}3\,$pc
and ${\sim}161$ M$_\odot$, respectively, NSCs naturally emerge in a subset of
our EDGE dwarfs with redshift-zero halo masses of $\rm{M}_{\rm{r}200\rm{c}}
\sim 5 \times 10^9$ M$_\odot$. These dwarfs are quenched by reionisation, but
retain a significant reservoir of gas that is unable to cool and form stars.
Sometime after reionisation, the dwarfs then undergo a major (${\sim}$1:1)
merger that excites rapid gas cooling, leading to a significant starburst. An
NSC forms in this starburst that then quenches star formation thereafter. The
result is a nucleated dwarf that has two stellar populations with distinct age:
one pre-reionisation and one post-reionisation. Our mechanism is unique for two
key reasons. Firstly, the low mass of the host dwarf means that NSCs, formed in
this way, can accrete onto galaxies of almost all masses, potentially seeding
the formation of NSCs everywhere. Secondly, our model predicts that NSCs should
have at least two stellar populations with a large ($\gtrsim$1 billion year)
age separation. This yields a predicted colour magnitude diagram for our
nucleated dwarfs that has two distinct main sequence turnoffs. Several GCs
orbiting the Milky Way, including Omega Centauri and M54, show exactly this
behaviour, suggesting that they may, in fact, be accreted NSCs.
