We have measured the 3d→2p transition x rays of kaonic ^{3}He and ^{4}He atoms using superconducting transition-edge-sensor microcalorimeters with an energy resolution better than 6 eV (FWHM). We determined the energies to be 6224.5±0.4(stat)±0.2(syst) eV and 6463.7±0.3(stat)±0.1(syst) eV, and widths to be 2.5±1.0(stat)±0.4(syst) eV and 1.0±0.6(stat)±0.3(stat) eV, for kaonic ^{3}He and ^{4}He, respectively. These values are nearly 10 times more precise than in previous measurements. Our results exclude the large strong-interaction shifts and widths that are suggested by a coupled-channel approach and agree with calculations based on optical-potential models.