Craig Lynch, 37, confessed to killing Sister Karen Klimczak but said it was an accident, police said. He was in police custody and was expected to be charged with second-degree murder and larceny.
The body of Klimczak, 62, was found behind an abandoned house about five miles from her home, said Detective Sgt. Jim Lonergan. It was in a shallow grave inside a shed, and it looked as if she might have been suffocated or strangled. There were no gun or knife wounds, he said.
Lynch had stolen Sister Karen Klimczak's cell phone Friday night and sold it to someone on the street, Lonergan said.
It was not immediately clear how the cell phone led police to Lynch.
Lynch had been living since April 5 in Hope House, a halfway house Klimczak founded in 1989 for nonviolent ex-convicts, police said. Authorities could provide few details on his criminal history but said he had stolen property in the past.
Police Commissioner H. McCarthy Gipson said that Lynch called the killing "an accident" and that he was in Klimczak's room trying to steal her cell phone when she came home Friday evening.
Lynch also confessed to being high on drugs, police said.
Klimczak was last seen Friday night at Bissonette House, where she lived. The residence is at the same address as Hope House.
Some of her clothing, the phone and other items were found in two trash bins near the home, Police Commissioner H. McCarthy Gipson said.
Church members became concerned when the nun missed several appointments Saturday and failed to show up for Easter services.