On Wednesday, Joe Alleva announced that he was stepping down and will transition into a new role at LSU.
Woodward is a native of Baton Rouge, Louisiana, and graduated from LSU. He served as the university's external affairs director from 2000 to 2004 before heading to the University of Washington, where he was promoted to AD in 2008 and served until 2015.
Woodward has been Texas A&M AD since 2016. He made splashy hires with Jimbo Fisher as football coach in 2017 and then Buzz Williams as basketball coach just this month.
Alleva, who had been LSU's athletic director since July 2008, will become the special assistant to the president for donor relations, the school announced Wednesday.
"We are grateful to Joe for his years of service and dedication to LSU," LSU president F. King Alexander said in a statement. "Under his leadership, LSU athletics has become even more nationally competitive, and our student-athletes have reached new levels of academic achievement."
The Tigers' basketball program has been a part of the FBI's ongoing investigation into corruption in the sport. Coach Will Wade was reinstated Sunday after being suspended toward the end of this season following reports that he was caught on a wiretap discussing a "strong-ass offer" for a recruit.
Many fans were upset with Alleva and the LSU administration for suspending Wade in the first place.
Sources told ESPN's Mark Schlabach that Wade's representatives were notified that the coach would be subpoenaed to testify in the basketball corruption trial later this month in New York. Wade has denied any wrongdoing.
Alleva also was criticized for the way he handled Les Miles' ouster as head football coach in 2016, as well as the search for Miles' replacement, which led to Ed Orgeron's promotion to full-time head coach after he served most of the 2016 season as interim head coach.
During Alleva's tenure, LSU won 18 Southeastern Conference titles.
"The eleven years Annie and I have been here in Baton Rouge have been some of the best in our lives," Alleva said Wednesday in a statement. "We have made lifelong friends and memories in Louisiana. This is truly a special place. It's been an honor to serve LSU, and I am proud to continue to do that in a new role."
His contract, which paid him $725,000 per year, was set to expire on June 30, 2020.