The school has announced a 4 p.m. ET press conference on Monday.
Morris will receive about $2 million a year, the Dallas Morning News reported.
A 1992 Texas A&M graduate and Texas native, Morris has been offensive coordinator/quarterbacks coach at Clemson since 2011. Morris will replace interim coach Tom Mason. Mason took over after June Jones resigned in September. The Mustangs, 0-11, close out the season Saturday at UConn.