Morrison got his start in 1966 working for the Saskatoon StarPhoenix before moving on to radio and then television. He was a reporter or anchor at local stations in Saskatchewan, Vancouver, British Columbia and Toronto, Ontario.

He joined CTV's Canada AM in 1973 as a newsreader and also worked as a reporter and weekend anchor as well as a Producer. As a reporter at CTV, he won awards for his coverage of the Yom Kippur War. From 1975 to 1976, he was a reporter on CTV National News and served as National Affairs Correspondent and substitute anchor on the show from 1976 to 1979.

In 1981, Morrison married Suzanne (née Langford) Perry, a Writer, consultant and political fund-raiser who was also Press Secretary to Canadian Prime Minister Pierre Trudeau. He became stepfather to Future Friends star Matthew Perry and, later, father to Caitlin (born 1981), Emily (born 1985), Willy (born 1987), and Madeleine (born 1989). He also has a son, Michael (born 1974), from a previous marriage.

Morrison joined the Canadian Broadcasting Corporation in 1982 as substitute anchor and Chief Political Correspondent for The Journal, the network's nightly public affairs program, remaining until 1986. He also co-hosted Midday, the network's noon-hour newsmagazine that he helped to create, from 1984 to 1985.

He moved to Los Angeles in 1986 as the 5pm and 11pm news anchor for KNBC-TV. In 1988 he joined NBC News as a west coast correspondent for the NBC Nightly News and Today Show. Morrison covered the Tiananmen Square protests of 1989 and later contributed hour-long documentaries and magazine segments to various NBC programs while concurrently continuing as KNBC's anchor.

Morrison returned to Canada in 1992 to become co-anchor of the leading national morning news program, Canada AM on CTV. He also hosted The Editors on PBS. He was the substitute anchor for CTV National News and the heir apparent to anchor Lloyd Robertson until 1995 when he was ousted in a network shakeup. It was believed, at the time, that he was campaigning to replace Robertson. While at Canada AM, then-Prime Minister Brian Mulroney cancelled a live appearance after Morrison jokingly referred to him earlier in the show as "whatshisname".

Morrison returned to NBC in 1995 and, since then, has covered a wide variety of stories on Dateline, from 9/11 to Columbine, from the peace process in the Middle East to tsunamis in the far east, from wars fought by child Soldiers in Africa to the medical miracles that keep other children alive, from the struggle to "Free Willy", to the battle waged over the fate of Elian Gonzales. Morrison has specialized in reporting "true mystery" stories for Dateline.

Morrison's reporting style has been parodied on Saturday Night Live by cast member Bill Hader. On the March 30, 2009, episode of Late Night with Jimmy Fallon, Hader, referencing the fact that Morrison works in the RCA Building, where both Dateline NBC and Saturday Night Live are produced, jokingly stated that he lived in fear of getting into the same elevator as Morrison.

On an episode of Late Night with Seth Meyers that aired on 9 July 2014, Morrison appears as himself, parodying his characteristic dramatic delivery of real-life murder mysteries that he is known for on Dateline.