We present a catalog of high redshift star-forming galaxies selected to lie within the redshift range z \simeq 7-8 using the Ultra Deep Field 2012 ( UDF12 ) , the deepest near-infrared ( near-IR ) exposures yet taken with the Hubble Space Telescope . As a result of the increased near-infrared exposure time compared to previous HST imaging in this field , we probe \sim 0.65 ( 0.25 ) mag fainter in absolute UV magnitude , at z \sim 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 drop-out selected UDF sources to 47 at z \sim 7 and 27 at z \sim 8 . Incorporating brighter archival and ground-based samples , we measure the z \simeq 7 UV luminosity function to an absolute magnitude limit of M _ { \mathrm { 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 \simeq 8 that takes account of our newly-added imaging in the F140W filter , and incorporating archival data from the HIPPIES and BoRG campaigns , we provide a robust estimate of the faint end slope at z \simeq 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 ( McLure et al 2012 ) .