This study was based on the contemporary proposal that distinct states of consciousness are quantifiable by neural complexity and critical dynamics. To test this hypothesis, it was aimed at comparing the electrophysiological correlates of three meditation conditions using nonlinear techniques from the complexity and criticality framework as well as power spectral density. Thirty participants highly proficient in meditation were measured with 64-channel electroencephalography (EEG) during one session consisting of a task-free baseline resting (eyes closed and eyes open), a reading condition, and three meditation conditions (thoughtless emptiness, presence monitoring, and focused attention). The data were analyzed applying analytical tools from criticality theory (detrended fluctuation analysis, neuronal avalanche analysis), complexity measures (multiscale entropy, Higuchi’s fractal dimension), and power spectral density. Task conditions were contrasted, and effect sizes were compared. Partial least square regression and receiver operating characteristics analysis were applied to determine the discrimination accuracy of each measure. Compared to resting with eyes closed, the meditation categories emptiness and focused attention showed higher values of entropy and fractal dimension. Long-range temporal correlations were declined in all meditation conditions. The critical exponent yielded the lowest values for focused attention and reading. The highest discrimination accuracy was found for the gamma band (0.83–0.98), the global power spectral density (0.78–0.96), and the sample entropy (0.86–0.90). Electrophysiological correlates of distinct meditation states were identified and the relationship between nonlinear complexity, critical brain dynamics, and spectral features was determined. The meditation states could be discriminated with nonlinear measures and quantified by the degree of neuronal complexity, long-range temporal correlations, and power law distributions in neuronal avalanches.