Abstract Progenitor models for the “luminous” subclass of Fast Blue Optical Transients (LFBOTs; prototype: AT2018cow) are challenged to simultaneously explain all of their observed properties: fast optical rise times of days or less; peak luminosities ≳10 44 erg s −1 ; low yields ≲0.1 M ⊙ of 56 Ni; aspherical ejecta with a wide velocity range (≲3000 km s −1 to ≳0.1–0.5 c with increasing polar latitude); presence of hydrogen-depleted-but-not-free dense circumstellar material (CSM) on radial scales from ∼10 14 cm to ∼3 × 10 16 cm; embedded variable source of non-thermal X-ray/ γ -rays, suggestive of a compact object. We show that all of these properties are consistent with the tidal disruption and hyper-accretion of a Wolf-Rayet (WR) star by a black hole or neutron star binary companion. In contrast with related previous models, the merger occurs with a long delay (≳100 yr) following the common envelope (CE) event responsible for birthing the binary, as a result of gradual angular momentum loss to a relic circumbinary disk. Disk-wind outflows from the merger-generated accretion flow generate the 56 Ni-poor aspherical ejecta with the requisite velocity range. The optical light curve is powered primarily by reprocessing X-rays from the inner accretion flow/jet, though CSM shock interaction also contributes. Primary CSM sources include WR mass loss from the earliest stages of the merger (≲10 14 cm) and the relic CE disk and its photoevaporation-driven wind (≳10 16 cm). Longer delayed mergers may instead give rise to supernovae Type Ibn/Icn (depending on the WR evolutionary state), connecting these transient classes with LFBOTs.