On the time scale of up to millennia the flux of cosmic rays outside the Heliosphere can be assumed roughly constant, and the cosmic-ray variability observed near Earth is driven by solar magnetic activity. Thus, using data on cosmogenic isotopes measured in natural terrestrial archives, past solar activity can be reconstructed. The most important cosmogenic isotopes are radiocarbon 14C and beryllium 10Be. However, because of the diversity of the proxy archives, it is difficult to build a homogeneous reconstruction, and previous studies showed inconsistencies with each other. Here we report a new consistent multi-proxy reconstruction of the cosmic-ray variability over the Holocene (last 9000 years), using all available long-span datasets of 10Be and 14C in terrestrial archives (six 10Be series of different ice cores from Greenland and Antarctica, as well as the global 14C production series). We have applied a new method, based on a Bayesian approach, which yields the most probable values of the solar modulation as well as straightforward estimates of the related uncertainties. The final reconstruction indicates the presence of a slow 6 – 7 millennia 'wave' in the long-term evolution of solar activity, with lows at ca. 5500 BC and 1000 AD. Two distinct components of solar activity were confirmed: the main component, corresponding to the "normal" moderate level, and a component corresponding to grand minima. A possible existence of a component representing grand maxima cannot be separated from the main component in a statistically significant manner.