  We generalize normal mode expansion of Green's tensor
$\bar{\bar{G}}(\bf{r},\bf{r}')$ to lossy resonators in open systems, resolving
a longstanding open challenge. We obtain a simple yet robust formulation,
whereby radiation of energy to infinity is captured by a complete, discrete set
of modes, rather than a continuum. This enables rapid simulations by providing
the spatial variation of $\bar{\bar{G}}(\bf{r},\bf{r}')$ over both $\bf{r}$ and
$\bf{r}'$ in one simulation. Few eigenmodes are often necessary for
nanostructures, facilitating both analytic calculations and unified insight
into computationally intensive phenomena such as Purcell enhancement, radiative
heat transfer, van der Waals forces, and F\"{o}rster resonance energy transfer.
We bypass all implementation and completeness issues associated with the
alternative quasinormal eigenmode methods, by defining modes with permittivity
rather than frequency as the eigenvalue. We obtain true stationary modes that
decay rather than diverge at infinity, and are trivially normalized.
Completeness is achieved both for sources located within the inclusion and the
background through use of the Lippmann-Schwinger equation. Modes are defined by
a linear eigenvalue problem, readily implemented using any numerical method. We
demonstrate its simple implementation on COMSOL Multiphysics, using the default
inbuilt tools. Results were validated against direct scattering simulations,
including analytical Mie theory, attaining arbitrarily accurate agreement
regardless of source location or detuning from resonance.
