Dispersed emission spectra collected upon the 4(2)P(3/2,1/2)<--4(2)S(1/2) optical excitation of K atoms attached to helium nanodroplets include broad, structured, red-shifted features which are shown to be due to K*He exciplex formation, paralleling our former observation of Na*He [J. Reho, C. Callegari, J. Higgins, W. E. Ernst, K. K. Lehmann, and G. Scoles, Discuss. Faraday Sec. 108, 161 (1997)]. The exciplex formation is demonstrated by the agreement obtained in comparing the K*He A(1) (II)-I-2 -->X(1) 2 Sigma emission spectra with the predictions derived from available nb initio potential energy surfaces. Recent analysis of both exciplex emissions also points to the possibility of triatomic (Na*He-2 and K*He-2) exciplex formation for a small fraction of the alkali atoms. The lack of fluorescence quenching, which is present when the spectra are taken in bulk liquid helium, is due to the surface location of the alkali atoms on the helium droplets that allows the nascent Na*He and K*He exciplexes to desorb from the droplet and emit as isolated molecules.