The first direct mass measurement of {6}He has been performed with the TITAN Penning trap mass spectrometer at the ISAC facility. In addition, the mass of {8}He was determined with improved precision over our previous measurement. The obtained masses are m({6}He)=6.018 885 883(57) u and m({8}He)=8.033 934 44(11) u. The {6}He value shows a deviation from the literature of 4σ. With these new mass values and the previously measured atomic isotope shifts we obtain charge radii of 2.060(8) and 1.959(16) fm for {6}He and {8}He, respectively. We present a detailed comparison to nuclear theory for {6}He, including new hyperspherical harmonics results. A correlation plot of the point-proton radius with the two-neutron separation energy demonstrates clearly the importance of three-nucleon forces.