  We estimate the expected event rate of gravitational wave signals from
mergers of supermassive black holes that could be resolved by a space-based
interferometer, such as the Evolved Laser Interferometer Space Antenna (eLISA),
utilising the reference cosmological hydrodynamical simulation from the EAGLE
suite. These simulations assume a $\Lambda$CDM cosmogony with state-of-the-art
subgrid models for radiative cooling, star formation, stellar mass loss, and
feedback from stars and accreting black holes. They have been shown to
reproduce the observed galaxy population with unprecedented fidelity. We
combine the merger rates of supermassive black holes in EAGLE with the latest
phenomenological waveform models to calculate the gravitational waves signals
from the intrinsic parameters of the merging black holes. The EAGLE models
predict $\sim2$ detections per year by a gravitational wave detector such as
eLISA. We find that these signals are largely dominated by mergers between seed
mass black holes merging at redshifts between $z\sim2$ and $z\sim1$. In order
to investigate the dependence on the assumed black hole seed mass, we introduce
an additional model with a black hole seed mass an order of magnitude smaller
than in our reference model. We also consider a variation of the reference
model where a prescription for the expected delays in the black hole merger
timescale has been included after their host galaxies merge. We find that the
merger rate is similar in all models, but that the initial black hole seed mass
could be distinguished through their detected gravitational waveforms. Hence,
the characteristic gravitational wave signals detected by eLISA will provide
profound insight into the origin of supermassive black holes and the initial
mass distribution of black hole seeds.
