We present the completed KMOS3D survey, an integral field spectroscopic survey of 739 \(\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 9\) 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 Hα, N ii, and S ii emission lines. We detect Hα 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 1 M ⊙ yr−1, as well as to resolve 81% of detected galaxies with ≥3 resolution elements along the kinematic major axis. The detection fraction of Hα 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 Hα and UV+IR star formation rates reveal that dust attenuation corrections may be underestimated by 0.5 dex at the highest masses (\(\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 10.5\)). We confirm our first year results of a high rotation-dominated fraction (monotonic velocity gradient and v rot/\({\sigma }_{0}\gt \sqrt{3.36}\)) of 77% for the full KMOS3D 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 \(\mathrm{log}({M}_{\star }/{M}_{\odot })\lt 10.5\). With this paper, we include a final data release of all 739 observed objects (http://www.mpe.mpg.de/ir/KMOS3D).