Abstract We present a catalog of central engine properties, i.e., black hole mass ( M BH ) and accretion luminosity ( L disk ), for a sample of 1077 blazars detected with the Fermi Large Area Telescope. This includes broad emission-line systems and blazars whose optical spectra lack emission lines but are dominated by the absorption features arising from the host galaxy. The average M BH for the sample is , and there is evidence suggesting the association of more massive black holes with absorption-line systems. Our results indicate a bimodality of L disk in Eddington units ( L disk / L Edd ) with broad-line objects tend to have a higher accretion rate ( L disk / L Edd > 0.01). We have found that L disk / L Edd and Compton dominance (CD; the ratio of the inverse Compton to synchrotron peak luminosities) are positively correlated at the >5 σ confidence level, suggesting that the latter can be used to reveal the state of accretion in blazars. Based on this result, we propose a CD-based classification scheme. Sources with CD > 1 can be classified as high-Compton-dominated or HCD blazars, whereas those with CD ≲ 1 are low-Compton-dominated (LCD) objects. This scheme is analogous to that based on the mass accretion rate proposed in the literature; however, it overcomes the limitation imposed by the difficulty in measuring L disk and M BH for objects with quasi-featureless spectra. We conclude that the overall physical properties of Fermi blazars are likely to be controlled by the accretion rate in Eddington units. The catalog is made public at http://www.ucm.es/blazars/engines and Zenodo.