  A metastable cosmic-string network is a generic consequence of many grand
unified theories (GUTs) when combined with cosmic inflation. Metastable cosmic
strings are not topologically stable, but decay on cosmic time scales due to
pair production of GUT monopoles. This leads to a network consisting of
metastable long strings on superhorizon scales as well as of string loops and
segments on subhorizon scales. We compute for the first time the complete
stochastic gravitational-wave background (SGWB) arising from all these network
constituents, including several technical improvements to both the derivation
of the loop and segment contributions. We find that the gravitational waves
emitted by string loops provide the main contribution to the gravitational-wave
spectrum in the relevant parameter space. The resulting spectrum is consistent
with the tentative signal observed by the NANOGrav and Parkes pulsar timing
collaborations for a string tension of G\mu ~ 10^-11...-7 and has ample
discovery space for ground- and space-based detectors. For GUT-scale string
tensions, G\mu ~ 10^-8...-7, metastable strings predict a SGWB in the
LIGO-Virgo-KAGRA band that could be discovered in the near future.
