We perform a cosmic shear analysis in harmonic space using the first year of data collected by the Dark Energy Survey (DES-Y1). We measure the cosmic weak lensing shear power spectra using the metacalibration catalogue and perform a likelihood analysis within the framework of CosmoSIS. We set scale cuts based on baryonic effects contamination and model redshift and shear calibration uncertainties as well as intrinsic alignments. We adopt as fiducial covariance matrix an analytical computation accounting for the mask geometry in the Gaussian term, including non-Gaussian contributions. A suite of 1200 lognormal simulations is used to validate the harmonic space pipeline and the covariance matrix. We perform a series of stress tests to gauge the robustness of the harmonic space analysis. Finally, we use the DES-Y1 pipeline in configuration space to perform a similar likelihood analysis and compare both results, demonstrating their compatibility in estimating the cosmological parameters S-8, sigma(8), and omega(m). We use the DES-Y1 metacalibration shape catalogue, with photometric redshifts estimates in the range of 0.2-1.3, divided in four tomographic bins finding sigma(8)(omega(m)/0.3)(0.5) = 0.766 +/- 0.033 at 68 per cent CL. The methods implemented and validated in this paper will allow us to perform a consistent harmonic space analysis in the upcoming DES data.