We present the completed KMOS^3D^ survey, an integral field spectroscopic survey of 739 log(M_*_/M_{sun}_)>9 galaxies at 0.6<z<2.7 using the K-band Multi Object Spectrograph (KMOS) at the Very Large Telescope. The KMOS3D survey provides a population-wide census of kinematics, star formation, outflows, and nebular gas conditions both on and off the star-forming galaxy main sequence through the spatially resolved and integrated properties of H{alpha}, [NII], and [SII] emission lines. We detect H{alpha} emission for 91% of galaxies on the main sequence of star formation and 79% overall. The depth of the survey has allowed us to detect galaxies with star formation rates below 1M_{sun}_/yr, as well as to resolve 81% of detected galaxies with >=3 resolution elements along the kinematic major axis. The detection fraction of H{alpha} is a strong function of both color and offset from the main sequence, with the detected and nondetected samples exhibiting different spectral energy distribution shapes. Comparison of H{alpha} and UV+IR star formation rates reveal that dust attenuation corrections may be underestimated by 0.5dex at the highest masses (log(M_*_/M_{sun}_)>10.5). We confirm our first year results of a high rotation-dominated fraction (monotonic velocity gradient and v_rot_/{sigma}_0_>3.36^0.5^) of 77% for the full KMOS^3D^ sample. The rotation-dominated fraction is a function of both stellar mass and redshift, with the strongest evolution measured over the redshift range of the survey for galaxies with log(M_*_/M_{sun}_)<10.5.