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In 2005, Morgan signed with Rocketown Records. The company released his debut album in the United States, but four of the original songs were removed in favour of cover versions of Hillsong songs written by Morgan. In addition, the remaining songs were remixed and the resulting songs had a heavier feel when compared to the softer adult contemporary-style originals.
Morgan has toured extensively around the United States, Canada and Europe. A 2007 European tour featured events in Scotland, England, Germany and Sweden.Everyone, contains Morgan's interpretation of his music and was mostly written in the previous 18 months, recorded in a big sounding, studio worship without the congregational elements found in the Hillsong Live albums.Everyone largely featured covers of previously released Hillsong songs written by Morgan and was released in Australia on 2 October 2006.
Morgan officially became Hillsong's new worship pastor in 2008, succeeding Darlene Zschech, however, Zschech continues to be a worship leader of the Hillsong Worship Team. On 29 June 2010, Hillsong Live released A Beautiful Exchange, an album featuring songs by Morgan. Morgan led Hillsong's 2010 tour of the United States, which kicked off on 21 July and included events in Dallas, Detroit and Los Angeles.