We present an overview of the HERschel Inventory of The Agents of Galaxy Evolution (HERITAGE) in the Magellanic Clouds project, which is a Herschel Space Observatory open time key program. We describe in detail the data processing, particularly for the PACS data, which required some custom steps because of the large angular extent of a single observational unit and overall the large amount of data to be processed as an ensemble. We report total global fluxes for the LMC and SMC and demonstrate their agreement with measurements by prior missions. We describe the point source extraction processing and the criteria used to establish a catalog for each waveband for the HERITAGE program. The 250 mu m band is the most sensitive and the source catalogs for this band have ~25,000 objects for the LMC and ~5500 objects for the SMC.