The measurement and understanding of collective solvation dynamics in DNA have vital biological implications, as protein and ligand binding to DNA can be directly controlled by complex electrostatic interactions of anionic DNA and surrounding dipolar water, and ions. Time-resolved fluorescence Stokes shift (TRFSS) experiments revealed anomalously slow solvation dynamics in DNA much beyond 100 ps that follow either power-law or slow multiexponential decay over several nanoseconds. The origin of such dispersed dynamics remains difficult to understand. Here we compare results of TRFSS experiments to molecular dynamics (MD) simulations of well-known 4',6-diamidino-2-phenylindole (DAPI)/Dickerson-Drew DNA complex over five decades of time from 100 fs to 10 ns to understand the origin of such dispersed dynamics. We show that the solvation time-correlation function (TCF) calculated from 200 ns simulation trajectory (total 800 ns) captures most features of slow dynamics as measured in TRFSS experiments. Decomposition of TCF into individual components unravels that slow dynamics originating from dynamically coupled DNA-water motion, although contribution from coupled water-Na+ motion is non-negligible. The analysis of residence time of water molecules around the probe (DAPI) reveals broad distribution from ∼6 ps to ∼3.5 ns: Several (49 nos.) water molecules show residences time greater than 500 ps, of which at least 14 water molecules show residence times of more than 1 ns in the first solvation shell of DAPI. Most of these slow water molecules are found to occupy two hydration sites in the minor groove near DAPI binding site. The residence time of Na+, however, is found to vary within ∼17-120 ps. Remarkably, we find that freezing the DNA fluctuations in simulation eliminates slower dynamics beyond ∼100 ps, where water and Na+ dynamics become faster, although strong anticorrelation exists between them. These results indicate that primary origin of slow dynamics lies within the slow fluctuations of DNA parts that couple with nearby slow water and ions to control the dispersed collective solvation dynamics in DNA minor groove.