We have measured the muon flux at the underground Gran Sasso National Laboratory (3800 m w.e.) to be (3.41 \pm 0.01) \times 10-4m-2s-1 using four years of Borexino data. A modulation of this signal is observed with a period of (366\pm3) days and a relative amplitude of (1.29 \pm 0.07)%. The measured phase is (179 \pm 6) days, corresponding to a maximum on the 28th of June. Using the most complete atmospheric data models available, muon rate fluctuations are shown to be positively correlated with atmospheric temperature, with an effective coefficient {\alpha}T = 0.93 \pm 0.04. This result represents the most precise study of the muon flux modulation for this site and is in good agreement with expectations.
