  Evidence is mounting that recent multiwavelength detections of fast blue
optical transients (FBOTs) in star-forming galaxies comprise a new class of
transients, whose origin is yet to be understood. We show that hydrogen-rich
collapsing stars that launch relativistic jets near the central engine can
naturally explain the entire set of FBOT observables. The jet-star interaction
forms a mildly-relativistic shocked jet (inner cocoon) component, which powers
cooling emission that dominates the high velocity optical signal during the
first few weeks, with a typical energy of $ \sim 10^{50}-10^{51} $ erg. During
this time, the cocoon radial energy distribution implies that the optical
lightcurve exhibits a fast decay of $ L \propto t^{-2.4} $. After a few weeks,
when the velocity of the emitting shell is $ \sim 0.01 $ c, the cocoon becomes
transparent, and the cooling envelope governs the emission. The interaction
between the cocoon and the dense circumstellar winds generates synchrotron
self-absorbed emission in the radio bands, featuring a steady rise on a month
timescale. After a few months the relativistic outflow decelerates, enters the
observer's line of sight, and powers the peak of the radio lightcurve, which
rapidly decays thereafter. The jet (and the inner cocoon) become optically thin
to X-rays $ \sim $ day after the collapse, allowing X-ray photons to diffuse
from the central engine that launched the jet to the observer. Cocoon cooling
emission is expected at higher volumetric rates than gamma-ray bursts (GRBs) by
a factor of a few, similar to FBOTs. We rule out uncollimated outflows, however
both GRB jets and failed collimated jets are compatible with all observables.
