  We study the gravitational wave (GW) phase shift arising from R{\o}mer delay
in binary black hole (BBH) mergers formed dynamically in three-body systems,
where both the inner orbit of the merging binary and the outer orbit are
eccentric. We provide a semi-analytical model and several analytical
approximations that allow for fast evaluation of both the temporal evolution
and the maximum value of the phase shift. The highest phase shifts occur when
the binary merges close to the pericentre of the outer orbit, and can in this
case be orders-of-magnitude larger compared to the circular limit. At high
outer orbit eccentricities, the orbital curvature leaves distinct imprints onto
the phase shift if the binary passes the outer pericentre during its inspiral.
By comparing with phase-shifts measured in numerical chaotic 3-body
scatterings, we show that our model accurately describes the observed phase of
dynamically assembled binary systems in realistic astrophysical scenarios,
providing a way to directly determine their formation channel via single GW
observations.
