Morton, 47, was thrown overboard as he negotiated some of the world’s most difficult rapids.
He was pulled from the icy water within minutes but could not be saved.
The tragedy happened during a 19-day trip, during which Steve, originally from Dunfermline, scaled Mount McKinley, North America’s tallest mountain peak.
The father-of-four relished challenges. A former Army man, he had climbed Kilimanjaro and competed in numerous sports.
Steve’s widow Vanessa Langlois, 51, said: “He had a sense of adventure and he was always planning the next thing. He was going to climb Everest next.”
The rafting tragedy happened in Six Mile Creek, 70 miles south-east of the capital Anchorage. Business analyst Steve, who lived in Cambridge, is thought to have suffered cold water shock.
A port mortem examination will confirm how he died.
Chuck Spaulding, of rafting firm Nova River Runners, said he was “still putting together the big picture”.