Condensation of monovalent counterions around DNA influences polymer properties of the DNA chain. For example, the Na+ ions show markedly stronger propensity to induce multiple DNA chains to assemble into compact structures compared with the K+ ions. To investigate the similarities and differences in the sodium and potassium ion condensation around DNA, we carried out a number of extensive all-atom molecular dynamics simulations of a DNA oligomer consisting of 16 base pairs, [d(CGAGGTTTAAAC-CTCG)]2, in explicit water. We found that the Na+ ions penetrate the DNA interior and condense around the DNA exterior to a significantly larger degree compared with the K+ ions. We have provided a microscopic explanation for the larger Na+ affinity toward DNA that is based on a combination of steric, electrostatic, and hydration effects. Unexpectedly, we found that the Cl- co-ions provide more efficient electrostatic screening for the K+ ions than for the Na+ ions, contributing to the larger Na+ condensation around DNA. To examine the importance of the discrete nature of water and ions, we also computed the counterion distributions from the mean-field electrostatic theory, demonstrating significant disagreements with the all-atom simulations. Prior experimental results on the relative extent of the Na+ and K+ condensation around DNA were somewhat contradictory. Recent DNA compaction experiments may be interpreted to suggest stronger Na+ condensation around DNA compared to K+, which is consistent with our simulations. We also provide a simple interpretation for the experimentally observed increase in DNA electrophoretic mobility in the alkali metal series, Li+ < Na+ < K+ < Rb+. We compare the DNA segment conformational preferences in various buffers with the proposed NMR models.