We present a comprehensive study on how well gravitational-wave signals of binary black holes (BBHs) with nonzero eccentricities can be recovered with state of the art model-independent waveform reconstruction and parameter estimation techniques. For this we use BayesWave, a Bayesian algorithm used by the LIGO–Virgo Collaboration for unmodeled reconstructions of signal waveforms and parameters. We used two different waveform models to produce simulated signals of BBHs with eccentric orbits and embed them in samples of simulated noise of design-sensitivity Advanced LIGO detectors. We studied the network overlaps and point estimates of central moments of signal waveforms recovered by BayesWave as a function of e, the eccentricity of the binary at 8 Hz orbital frequency. BayesWave recovers signals of near-circular (e lesssim 0.2) and highly eccentric (e gsim 0.7) binaries with network overlaps similar to that of circular (e = 0) ones, however it produces lower network overlaps for binaries with e ∈ [0.2, 0.7]. Estimation errors on central frequencies and bandwidths (measured relative to bandwidths) are nearly independent from e, while estimation errors on central times and durations (measured relative to durations) increase and decrease with e above e gsim 0.5, respectively. We also tested how BayesWave performs when reconstructions are carried out using generalized wavelets with linear frequency evolution (chirplets) instead of sine-Gaussian wavelets. We have found that network overlaps improve by ~10–20 percent when chirplets are used, and the improvement is the highest at low (e < 0.5) eccentricities. There is however no significant change in the estimation errors of central moments when the chirplet base is used.