The interaction of light with nanometer-sized solids provides the means of focusing optical radiation to sub-wavelength spatial scales with associated electric field enhancements offering new opportunities for multifaceted applications. We utilize collective effects in nanoplasmas with sub-two-cycle light pulses of extreme intensity to extend the waveform-dependent electron acceleration regime into the relativistic realm, by using 106 times higher intensity than previous works to date. Through irradiation of nanometric tungsten needles, we obtain multi-MeV energy electron bunches, whose energy and direction can be steered by the combined effect of the induced near-field and the laser field. We identified a two-step mechanism for the electron acceleration: (i) ejection within a sub-half-optical-cycle into the near-field from the target at >TVm-1 acceleration fields, and (ii) subsequent acceleration in vacuum by the intense laser field. Our observations raise the prospect of isolating and controlling relativistic attosecond electron bunches, and pave the way for next generation electron and photon sources.