The Crown Prosecution Service (CPS) says it is also discontinuing proceedings against a friend of Morris, Kristofer Dickie.
The pair were arrested in October after an allegation made by a 20-year-old woman in Leeds.
The CPS said there was no realistic prospect of obtaining a conviction after examining the police file.
Neil Franklin of the CPS in West Yorkshire said he was confident that the police were right to charge the two men but new information had since been found.
"The CPS has a duty to keep cases under review and when fresh evidence comes to light, as it has here, we have to look at the case and decide whether it should still go ahead," he said.
"Having looked at this further evidence we have decided the case should not proceed."
Morris and Dickie were due to appear at Leeds Crown Court on 10 March.