RICHMOND — Gov. Robert F. McDonnell announced Monday that the state’s homeless population had dropped by 16 percent over the past three years, surpassing a goal set early in his administration.

Not long after taking office, McDonnell (R) pledged to reduce homelessness by 15 percent by 2013. It has fallen by 16 percent overall, by 17 percent for families and by 18 percent for veterans, McDonnell said. The last of those groups was a special focus for McDonnell, a veteran and whose daughter served with the Army in Iraq.

The reductions were achieved, in part, by shifting resources to “rapid re-housing” programs, which quickly place people in permanent housing instead of shelters, McDonnell said.

“Preventing and ending homelessness is a significant component of our ongoing efforts to build a healthy and prosperous commonwealth,” McDonnell said.