We present the completed KMOS$^mathrm{3D}$ survey $-$ an integral field spectroscopic survey of 739, $log(M_{star}/M_{odot})>9$, galaxies at $0.6<z<2.7$ using the K-band Multi Object Spectrograph (KMOS) at the Very Large Telescope (VLT). KMOS$^mathrm{3D}$ 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$alpha$, [N II], and [S II] 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 1 M$_{odot}$/ yr$^{-1}$, as well as to resolve 81% of detected galaxies with $geq3$ 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 non-detected samples exhibiting different SED shapes. Comparison of H$alpha$ and UV+IR star formation rates (SFRs) reveal that dust attenuation corrections may be underestimated by 0.5 dex at the highest masses ($log(M_{star}/M_{odot})>10.5$). We confirm our first year results of a high rotation dominated fraction (monotonic velocity gradient and $v_mathrm{rot}$/$sigma_0 > sqrt{3.36}$) of 77% for the full KMOS$^mathrm{3D}$ H$alpha$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 $log(M_{star}/M_{odot})<10.5$. With this paper we include a final data release of all 739 observed objects.
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