Upcoming LIGO-Virgo-KAGRA (LVK) observing runs are expected to detect a variety of inspiralling gravitational-wave (GW) events that come from black hole and neutron star binary mergers. Detection of noninspiral GW sources is also anticipated. We report the discovery of a new class of noninspiral GW sources—the end states of massive stars—that can produce the brightest simulated stochastic GW burst signal in the LVK bands known to date, and could be detectable in LVK run A+. Some dying massive stars launch bipolar relativistic jets, which inflate a turbulent energetic bubble—cocoon—inside of the star. We simulate such a system using state-of-the-art 3D general relativistic magnetohydrodynamic simulations and show that these cocoons emit quasi-isotropic GW emission in the LVK band, ∼10-100 Hz, over a characteristic jet activity timescale ∼10-100 s. Our first-principles simulations show that jets exhibit a wobbling behavior, in which case cocoon-powered GWs might be detected already in LVK run A+, but it is more likely that these GWs will be detected by the third-generation GW detectors with an estimated rate of ∼10 events yr−1. The detection rate drops to ∼1% of that value if all jets were to feature a traditional axisymmetric structure instead of a wobble. Accompanied by electromagnetic emission from the energetic core-collapse supernova and the cocoon, we predict that collapsars are powerful multimessenger events.