Interim coach Jeff Stoutland made the announcement Thursday, saying Harris puts the Hurricanes in the best position for a victory Friday.
He says Morris, who was hurt in Tuesday's practice, will be available if needed. Morris started the last four games for Miami.
Harris missed three games after a concussion against Virginia on Oct. 30. He replaced Morris in an overtime loss to South Florida on Nov. 27, throwing an interception late in regulation that kept Miami from trying what could have been a game-winning field goal.