Re-observations with the HESS telescope array of the very high-energy (VHE) source HESS J1018-589A that is coincident with the Fermi-LAT gamma-ray binary 1FGL J1018.6-5856 have resulted in a source detection significance of more than 9 sigma and the detection of variability (chi(2)/nu of 238.3/155) in the emitted gamma-ray flux. This variability confirms the association of HESS J1018-589A with the high-energy gamma-ray binary detected Fermi-LAT and also confirms the point-like source as a new VHE binary system. The spectrum of HESS J1018-589A is best fit with a power-law function with photon index Gamma = 2.20 +/- 0.14(stat) +/- 0.2(sys). Emission is detected up to similar to 20 TeV. The mean differential flux level is (2.9 +/- 0.4) x 10(-13) TeV-1 cm(-2) s(-1) at 1 TeV, equivalent to similar to 1% of the flux from the Crab Nebula at the same energy. Variability is clearly detected the night-by-night light curve. When folded on the orbital period of 16.58 days, the rebinned light curve peaks in phase with the observed X-ray high-energy phaseograms. The fit of the HESS phaseogram to a constant flux provides evidence of periodicity at the level of N-sigma > 3 sigma. The of the VHE phaseogram and measured spectrum suggest a low-inclination, low-eccentricity system with a modest impact from VHE gamma-ray due to pair production (tau less than or similar to 1 at 300 GeV).
