  Compact binaries that emit gravitational waves in the sensitivity band of
ground-based detectors can have non-negligible eccentricities just prior to
merger, depending on the formation scenario. We develop a purely analytic,
frequency-domain model for gravitational waves emitted by compact binaries on
orbits with small eccentricity, which reduces to the quasi-circular
post-Newtonian approximant TaylorF2 at zero eccentricity and to the
post-circular approximation of Yunes et al. (2009) at small eccentricity. Our
model uses a spectral approximation to the (post-Newtonian) Kepler problem to
model the orbital phase as a function of frequency, accounting for eccentricity
effects up to ${\cal{O}}(e^8)$ at each post-Newtonian order. Our approach
accurately reproduces an alternative time-domain eccentric waveform model for
eccentricities $e\in [0, 0.4]$ and binaries with total mass less than 12 solar
masses. As an application, we evaluate the signal amplitude that eccentric
binaries produce in different networks of existing and forthcoming
gravitational waves detectors. Assuming a population of eccentric systems
containing black holes and neutron stars that is uniformly distributed in
co-moving volume, we estimate that second generation detectors like Advanced
LIGO could detect approximately 0.1-10 events per year out to redshift $z\sim
0.2$, while an array of Einstein Telescope detectors could detect hundreds of
events per year to redshift $z \sim 2.3$.
