The dependences of the fluorescence intensity and anisotropy of molecular rotors SYBR Green (SG) and double-stranded DNA with 10, 20, and 100 base pairs on their relative concentration in solutions, as well as on the viscosity of the medium, were studied. It was shown that an increase in the fluorescence intensity with an increase in the SG concentration and subsequent reaching a constant value is associated with an initial increase in the number of SG molecules intercalated in DNA and a further process of saturation and the formation of nonfluorescent states. To explain the sharp drop in fluorescence anisotropy due to the Förster intramolecular energy transfer between DNA-bound SG molecules, a generalized model was developed that takes into account both internal rotations and rotational diffusion of molecular complex as a whole. The proposed model made it possible to calculate universally the obtained experimental dependences of the fluorescence anisotropy on the viscosity of the medium at various dye/DNA ratios and to estimate the Förster energy transfer rates.