The change will take place at the end of August, The Wall Street Journal reported Saturday.
Surma will become executive chairman, but only until the end of the year, when he will retire, the Pittsburgh Tribune-Review reported.
The firm said Chief Financial Officer and Executive Vice President Gretchen Haggerty will retire at the end of the month, and will be replaced by David Burritt, who previously served as CFO and vice president of global finance and strategic services for Caterpillar Inc. from 2004 to 2010.
"Dave joins our company as an extremely seasoned and highly regarded financial executive with strong leadership capabilities, a reputation for delivering results in complex and dynamic business and economic environments, and shares with us a commitment to leading with ethics and integrity," Surma said in a statement.
The Journal reported U.S. Steel is trying to dig its way out of a rut, having lost money in five of the past seven quarters.
The 112-year-old company lost $78 million in the second quarter and is up against a slow economic recovery, high labor costs, a rigid company structure and a global glut of steel, the Journal said.