In this study, fly ash (FA) compacts were prepared by accelerated carbonation as a potential sustainable building material application with the locally available ashes (oil shale ash (OSA), wood ash (WA) and land filled oil shale ash (LFA)) of Estonia. The carbonation behaviour of FAs and the performance of 100% FA based compacts were evaluated based on the obtained values of CO2 uptake and compressive strength. The influence of different variables (compaction pressure, curing temperature, CO2 concentration, and pressure) on the CO2 uptake and strength development of FA compacts were investigated and the reaction kinetics of the carbonation process were tested by different reaction-order models. A reasonable relation was noted between the CO2 uptake and compressive strength of the compacts. The porous surface structure of the hydrated OSA and WA compacts was changed after carbonation due to the calcite formations (being the primary carbonation product), especially on portlandite crystals. The increase of temperature, gas pressure, and CO2 concentration improved the CO2 uptake levels of compacts. However, the positive effect of increasing compaction pressure was more apparent on the final strength of the compacts. The obtained compressive strength and CO2 uptake values of FA compacts were between 10 and 36 MPa and 11 and 13 wt%, respectively, under various operation conditions. Moreover, compacts with mixed design (OSA/LFA and WA/LFA) resulted in low-strength and density compared to the single behaviour of OSA and WA compacts, yet a higher CO2 uptake was achieved (approximately 15% mass) with mixed design. The conformity of Jander equation (3D-diffusion-limited reaction model) was higher compared to other tested reaction order models for the representation of the carbonation reaction mechanism of OSA and WA. The activation energy for OSA compact was calculated as 3.55 kJ/mol and for WA as 17.06 kJ/mol.