Numerical relativity simulations provide the most precise templates for the gravitational waves produced by binary black hole mergers. However, many of these simulations use an incomplete waveform extraction technique – extrapolation – that fails to capture important physics, such as gravitational memory effects. Cauchy-characteristic evolution (CCE), by contrast, is a much more physically accurate extraction procedure that fully evolves Einstein’s equations to future null infinity and accurately captures the expected physics. In this work, we present a new surrogate model, NRHybSur3dq8_CCE, built from CCE waveforms that have been mapped to the post-Newtonian (PN) BMS frame and then hybridized with PN and effective one-body (EOB) waveforms. This model is trained on 102 waveforms with mass ratios q≤8 and aligned spins χ1z,χ2z ∈ [−0.8,0.8]. The model spans the entire LIGO-Virgo-KAGRA (LVK) frequency band (with flow=20Hz) for total masses M ≳ 2.25M⊙ and includes the ℓ≤4 and (ℓ,m)=(5,5) spin-weight −2 spherical harmonic modes, but not the (3,1), (4,2) or (4,1) modes. We find that NRHybSur3dq8_CCE can accurately reproduce the training waveforms with mismatches ≲ 2×10−4 for total masses 2.25M⊙ ≤ M ≤ 300M⊙ and can, for a modest degree of extrapolation, capably model outside of its training region. Most importantly, unlike previous waveform models, the new surrogate model successfully captures memory effects.