Conjugates of carbon nanoparticles and aptamers have great potential in many areas of biomedicine. In order to be implemented in practice, such conjugates should keep their properties throughout long storage period in commonly available conditions. In this work, we prepared conjugates of carbon nanoparticles (CNP) with DNA aptamers using streptavidin–biotin reaction. Obtained conjugates possess superior stability and kept their physical–chemical and functional properties during 30 days at +4 °C and −20 °C. Proposed approach to conjugation allows loading of about 100–120 pM of biotinylated aptamer per 1 mg of streptavidin-coated CNP (CNP–Str). Aptamer-functionalized CNP–Str have zeta potential of −34 mV at pH 7, mean diameter of 168–177 nm, and polydispersity index of 0.080–0.140. High reproducibility of functionalization was confirmed by preparation of several batches of CNP–aptamer with the same size distribution and aptamer loading using independently synthesized parent CNP–Str nanoparticles. Stability of CNP–aptamer conjugates was significantly enhanced by postsynthesis addition of EDTA that prevents nuclease degradation of immobilized aptamers. Obtained nanoparticles were stable at pH ranging from 6 to 10. Optical properties of CNP–aptamer nanoparticles were also studied and their ability to quench fluorescence via Förster resonance energy transfer was shown. Taking into account properties of CNP–aptamer conjugates, we suppose they may be used in both homo- and heterogeneous colorimetric, fluorescent, and aggregation-based assays.