The question "what is the observable electromagnetic (EM) signature of a compact binary merger?" is an intriguing one with crucial consequences to the quest for gravitational waves (GW). Compact binary mergers are prime sources of GW, targeted by current and next generation detectors. Numerical simulations have demonstrated that these mergers eject energetic sub-relativistic (or even relativistic) outflows. This is certainly the case if the mergers produce short GRBs, but even if not, significant outflows are expected. The interaction of such outflows with the surround matter inevitably leads to a long lasting radio signal. We calculate the expected signal from these outflows (our calculations are also applicable to short GRB orphan afterglows) and we discuss their detectability. We show that the optimal search for such signal should, conveniently, take place around 1.4 GHz. Realistic estimates of the outflow parameters yield signals of a few hundred µJy, lasting a few weeks, from sources at the detection horizon of advanced GW detectors. Followup radio observations, triggered by GW detection, could reveal the radio remnant even under unfavorable conditions. Upcoming all sky surveys can detect a few dozen, and possibly even thousands, merger remnants at any give time, thereby providing robust merger rate estimates even before the advanced GW detectors become operational. In fact, the radio transient RT 19870422 fits well the overall properties predicted by our model and we suggest that its most probable origin is a compact binary merger radio remnant.