The system announced Woodley's appointment Friday in a news release. Woodley succeeds Randy Moffett, who retired in September.
Woodley takes over on Jan. 1. She is leaving her job as vice chancellor for strategic initiatives at the University of Texas System.
The UL system includes Southeastern Louisiana University, UL-Lafayette, UL-Monroe, the University of New Orleans, McNeese State, Nicholls State, Louisiana Tech, Grambling State and Northwestern State.