Doxorubicin (DOX) is a cancer drug that binds to dsDNA through intercalation. A comprehensive microsecond timescale molecular dynamics study is performed for DOX with 16 tetradecamer dsDNA sequences in explicit aqueous solvent, in order to investigate the intercalation process at both binding stages (conformational change and insertion binding stages). The molecular mechanics generalized Born surface area (MM-GBSA) method is adapted to quantify and break down the binding free energy (BFE) into its thermodynamic components, for a variety of different solution conditions as well as different DNA sequences. Our results show that the van der Waals interaction provides the largest contribution to the BFE at each stage of binding. The sequence selectivity depends mainly on the base pairs located downstream from the DOX intercalation site, with a preference for (AT)2 or (TA)2 driven by the favorable electrostatic and/or van der Waals interactions. Invoking the quartet sequence model proved to be most successful to predict the sequence selectivity. Our findings also indicate that the aqueous bathing solution (i.e., water and ions) opposes the formation of the DOX-DNA complex at every binding stage, thus implying that the complexation process preferably occurs at low ionic strength and is crucially dependent on solvent effects.