We have studied the spectral luminescent properties of complexes of Tb(III) ions with a series of new derivatives of 2-oxo-4-hydroxyquinoline-3-carboxylic acid amides (L1–L4). We have established that DNA significantly enhances the 4f luminescence of terbium(III) in these complex compounds. We show satisfactory agreement between the logarithms of the DNA binding constants for a series of aminoalkoxy fluorenones (R1–R6), obtained using ethidium bromide and the complex Tb(III)-L1, which we propose using as a new luminescent probe for studying the affinity of drugs (prodrugs) for DNA molecules in a series of structurally similar biologically active substances.