We have measured the muon flux at the underground Gran Sasso National Laboratory (3800 m w.e.) to be (3.41 + or - 0.01) times 10 super(-4)m super(-2)s super(-1) using four years of Borexino data. A modulation of this signal is observed with a period of (366 + or - 3) days and a relative amplitude of (1.29 + or - 0.07)%. The measured phase is (179 + or - 6) days, corresponding to a maximum on the 28 super(th) 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 sub(T) = 0.93 + or - 0.04. This result represents the most precise study of the muon flux modulation for this site and is in good agreement with expectations.