Dual-comb spectroscopy is a rapidly developing spectroscopic technique that does not require any opto-mechanical moving parts and enables broadband and high-resolution measurements with microsecond time resolution. However, for high sensitivity measurements and extended averaging times, high mutual coherence of the comb-sources is essential. To date, most dual-comb systems employ coherent averaging schemes that require additional electro-optical components, which increase system complexity and cost. More recently, computational phase correction approaches that enables coherent averaging of spectra generated by free-running systems have gained increasing interest. Here, we propose such an all-computational solution that is compatible with real-time data acquisition architectures for free-running systems. The efficacy of our coherent averaging algorithm is demonstrated using dual-comb spectrometers based on quantum cascade lasers, interband cascade lasers, mode-locked lasers, and optically-pumped microresonators.