We present a time domain waveform model that describes the inspiral , merger and ringdown of compact binary systems whose components are non-spinning , and which evolve on orbits with low to moderate eccentricity . The inspiral evolution is described using third order post-Newtonian equations both for the equations of motion of the binary , and its far-zone radiation field . This latter component also includes instantaneous , tails and tails-of-tails contributions , and a contribution due to non-linear memory . This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian order in the zero eccentricity limit . To improve phase accuracy , we also incorporate higher-order post-Newtonian corrections for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries . This enhanced prescription for the inspiral evolution is combined with a fully analytical prescription for the merger-ringdown evolution constructed using a catalog of numerical relativity simulations . We show that this inspiral-merger-ringdown waveform model reproduces the effective-one-body model of Ref . [ Y. Pan et al . , Phys . Rev . D 89 , 061501 ( 2014 ) ] for quasi-circular black hole binaries with mass-ratios between 1 to 15 in the zero eccentricity limit over a wide range of the parameter space under consideration . Using a set of eccentric numerical relativity simulations , not used during calibration , we show that our new eccentric model reproduces the true features of eccentric compact binary coalescence throughout merger . We use this model to show that the gravitational wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasi-circular , spin-aligned waveforms if the eccentricity e _ { 0 } of these systems when they enter the aLIGO band at a gravitational wave frequency of 14 Hz satisfies e _ { 0 } ^ { GW 150914 } \leq 0.15 and e _ { 0 } ^ { GW 151226 } \leq 0.1 . We also find that varying the spin combinations of the quasi-circular , spin-aligned template waveforms does not improve the recovery of non-spinning , eccentric signals when e _ { 0 } \geq 0.1 . This suggests that these two signal manifolds are predominantly orthogonal .