Judgment aggregation (JA) offers a generic formal logical framework for modeling various settings where agents must reach joint agreements through aggregating the preferences, judgments, or beliefs of individual agents by social choice mechanisms. In this work, we develop practical JA algorithms for outcome determination by harnessing Boolean satisfiability (SAT) based solvers as the underlying reasoning engines, leveraging on their ability to efficiently reason over logical representations incrementally. Concretely, we provide algorithms for outcome determination under a range of aggregation rules, using natural choices of SAT-based techniques adhering to the computational complexity of the problem for the individual rules. We also implement and empirically evaluate the approach using both synthetic and PrefLib data, showing that the approach can scale significantly beyond recently proposed alternative algorithms for JA.