BBC Local Radio station is where Morris began his career. In the early 1990s, Morris teamed up with Armando Iannucci who is his radio producer to create a satire of new programmes titled On The Hour and which was later expanded into a television spin off, The Day Today. This program has since been hailed as one of the most important satirical shows of the 1990s. Morris further developed the satirical news format with Brass Eye focusing on themes such as crime and drugs, and which lampooned celebrities. A Brass Eye special, which dealt with the moral panic surrounding paedophilia quickly became one of the most complained about programmes in British television history. He was then described as "the most loathed man on TV" by the Daily Mail.
Morris's postmodern sketch radio show Blue Jam helped him to gain a cult following. After expanding a Blue Jam sketch into My Wrongs 8245-8249 & 117, he won a BAFTA for Best Short Film. He also created a sitcom titled as Nathan Barley in collaboration with Charlier Brooker that satirised hipsters. And he also joined the cast of the Graham Linehan sitcom The IT Crowd which was his first project that he did not have writing or producing input.
In 2010, Morris directed Four Lions, his first feature-length film which satirised Islamic terrorism through a group of inept British Pakistanis. The film has largely positive reception earning Morris his second BAFTA, for "Outstanding Debut". Since 2012, he has directed three episodes of Iannucci's political comedy Veep.