We present a catalog of high-redshift star-forming galaxies selected to lie within the redshift range z ~= 7-8 using the Ultra Deep Field 2012 (UDF12), the deepest near-infrared (near-IR) exposures yet taken with the Hubble Space Telescope (HST). As a result of the increased near-IR exposure time compared to previous HST imaging in this field, we probe ~0.65 (0.25) mag fainter in absolute UV magnitude, at z ~ 7 (8), which increases confidence in a measurement of the faint end slope of the galaxy luminosity function. Through a 0.7 mag deeper limit in the key F105W filter that encompasses or lies just longward of the Lyman break, we also achieve a much-refined color-color selection that balances high redshift completeness and a low expected contamination fraction. We improve the number of dropout-selected UDF sources to 47 at z ~ 7 and 27 at z ~ 8. Incorporating brighter archival and ground-based samples, we measure the z ~= 7 UV luminosity function to an absolute magnitude limit of M _UV = -17 and find a faint end Schechter slope of \alpha =-1.87^{+0.18}_{-0.17}. Using a similar color-color selection at z ~= 8 that takes our newly added imaging in the F140W filter into account, and incorporating archival data from the HIPPIES and BoRG campaigns, we provide a robust estimate of the faint end slope at z ~= 8, \alpha =-1.94^{+0.21}_{-0.24}. We briefly discuss our results in the context of earlier work and that derived using the same UDF12 data but with an independent photometric redshift technique.