We present the results from an X-ray spectral analysis of active galactic nuclei (AGN) in the Chandra Deep Field-South, All-wavelength Extended Groth-strip International Survey (AEGIS)-Deep X-ray survey (XD) and Chandra-Cosmic Evolution Surveys (COSMOS), focusing on the identification and characterization of the most heavily obscured, Compton thick (CT, NH>10^24^cm^-2^) sources. Our sample is comprised of 3184 X-ray selected extragalactic sources, which has a high rate of redshift completeness (96.6 per cent), and includes additional spectroscopic redshifts and improved photometric redshifts over previous studies. We use spectral models designed for heavily obscured AGN which self-consistently include all major spectral signatures of heavy absorption. We validate our spectral fitting method through simulations, identify CT sources not selected through this method using X-ray colours and take considerations for the constraints on NH given the low count nature of many of our sources. After these considerations, we identify a total of 100 CT AGN with best-fitting NH >10^24^cm^-2^ and NH constrained to be above 10^23.5^cm^-2^ at 90 per cent confidence. These sources cover an intrinsic 2-10keV X-ray luminosity range of 10^42^-3x10^45^erg/s and a redshift range of z=0.1-4. This sample will enable characterization of these heavily obscured AGN across cosmic time and to ascertain their cosmological significance. These survey fields are sites of extensive multiwavelength coverage, including near-infrared Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) data and far-infrared Herschel data, enabling forthcoming investigations into the host properties of CT AGN. Furthermore, by using the torus models to test different covering factor scenarios, and by investigating the inclusion of the soft scattered emission, we find evidence that the covering factor of the obscuring material decreases with LX for all redshifts, consistent with the receding torus model, and that this factor increases with redshift, consistent with an increase in the obscured fraction towards higher redshifts. The strong relationship between the parameters of obscuration and LX points towards an origin intrinsic to the AGN; however, the increase of the covering factor with redshift may point towards contributions to the obscuration by the host galaxy. We make NH, {GAMMA} (with uncertainties), observed X-ray fluxes and intrinsic 2-10keV luminosities for all sources analysed in this work publicly available in an online catalogue.