Some contend that Jesse James was not killed on 3 April, 1882, but lived and went on to father more children.
The team of 15 scientists hopes to determine the calibre of the bullet that killed him and the angle and distance from which it was fired. History has held that James was shot in St Joseph by Bob Ford, a member of James's gang who killed him to collect a bounty on his head. The inquiry may also reveal whether Ford acted alone or whether his brother, Charles, fired at the same time.
James had apparently been living under the alias of Tom Howard and posing as a cattle rancher. His supposed remains were moved from his mother's backyard, outside Kearney, Montana, to the Mount Olivet Cemetery in the town in 1902.
The results of an autopsy have been missing for years and the scientific team have asked three descendants to donate blood for DNA tests.
Robert Jackson, a great-great nephew of James's sister, was one of the relatives present at the hearing in Clay County court that has permitted the exhumation. "It's exciting," he said after the decision. "A lot of people say they are related to Jesse James. I always wondered why I had a compulsion to rob banks but became a lawyer."
Mr Jackson also wondered why so many people are eager to link themselves with the outlaw. "I guess infamy is better than nothing," he said.
Engineering Animation Inc, a computer graphics company, said the project would resolve doubts about the fate of the bandit. The company has previously investigated the death in 1953 of CIA scientist Frank Olson, who died while being given LSD without his knowledge.