Chicago Mayor Rahm Emanuel made the announcement Thursday. He says Woodyard has focused on sound financial management, among other things. Woodyard has been the CEO of the Charlotte Housing Authority since 2002.
The Charlotte Housing Authority's website says Woodyard is leaving his post for a job in Chicago and a spokeswoman said Woodyard tendered his resignation to the board earlier this month.
Long-time resident of the CHA-run Cabrini Green row houses, Michael McClaren, is unhappy with the choice.
"I know there's a lot of talented people here in Chicago that can fulfill that job and I don't understand why he doesn't choose someone who is familiar with the CHA problem and the transformation plan that they have put in place," McClaren said.
Emanuel has picked other outsiders for major city jobs like Chicago Public Schools CEO Jean Claude Brizard from New York and Chicago Police Superintendent Garry McCarthy from New Jersey.
Woodyard will replace the last CHA chief Lewis Jordan who resigned under a cloud of scrutiny. Jordan faced heavy questions about his credit card use at the city agency.
"I hope he can do better than what they're doing now, what they were doing," said Cabrini Green resident Jovanah Windbush.
Woodyard will assume a very tough job here in Chicago as the CHA is currently undergoing an ambitious public housing redevelopment effort, which is called The Plan for Transformation. The agency is redeveloping or rehabilitating its entire stock of public housing.
"He might make positive change but my problem is that by the time he learns what to do, they gonna get rid of him. He doesn't know the politics of Chicago," McClaren said.
The Associated Press contributed to this report.