The Borexino detector at Gran Sasso has now accumulated over ten years of continuous data which represent a magnificent opportunity to study the cosmic muon flux at a deep underground location. We present here a precision measurement of the flux and of the expected seasonal modulation. We present the correlation with the atmospheric temperature variations from global atmospheric models. We measure the correlation parameters and infer the kaon-to-pion ratio in the production of cosmic muons from high energy primaries. We also find evidence of a long term modulation that is not present in the atmospheric data and we investigate a possible positive correlation with the solar activity. Finally we observe a seasonal modulation of the production rate of cosmogenic neutrons that is in phase with the muon modulation but shows a surprisingly larger amplitude.