Morris joined the University of California, Davis, where he was awarded a President's Postdoctoral Fellowship. At UC Davis, Morris studied the dynamics of free radical systems. In 1996 Morris moved to Howard University, where he was appointed deputy director of the Center for the Study of Terrestrial and Extraterrestrial Atmospheres. His research looks to understand how atmospheric particulates influence the atmosphere and climate across multiple spatio-temporal scales. He served as Director of the Howard University component of the Goddard Space Flight Center Earth Science and Technology Center. In this capacity, Morris spent two years at Goddard, where he studied the movement of aerosols and dust from Asia across the Pacific Ocean.
At Howard University, Morris was the founding director of the National Oceanic and Atmospheric Administration (NOAA) Cooperative Science Center in Atmospheric Sciences and Meteorology. His research considered trace gases and aerosols in the urban environment. To understand the impact of these at a global scale, Morris directed several observation missions on board the NOAA Ship Ronald H. Brown. Amongst these missions were the AERosols and Oceanographic Science Expeditions (AEROSE), which involved investigations into the air mass outflows of Africa. These outflows included particulates from the Sahara desert and aerosols from the burning of biomass due to slash-and-burn agriculture. Such aerosols can influence the transfer of microbes across hemispheres (microbiological transfer), which can impact cloud formation and precipitation. Through these investigations Morris was able to create the world's most comprehensive data set of atmospheric measurements and oceanographic information. These studies permit the characterisation of the environmental impacts of Saharan dust aerosols as they move across the Atlantic Ocean.
In July 2020 Morris joined the faculty at Arizona State University as the Director of the School of Mathematical and Natural Sciences at the New College of Interdisciplinary Arts and Sciences.