Just to unpack "electronic signals", what propagates is the disturbance ("signal"), not the electrons themselves. Like waves propagating at the beach, where water only moves back and forth a little, and slower.
And specifically what causes the electrons to move each other is the electromagnetic field. The boson of the electromagnetic field is the photon, so the signal is being carried from one electron to the next by photons. (Although the disturbance itself as a whole is not a photon; I think it's often described as a quasiparticle called a plasmon.)