Javon Tyrek Rogers was arrested Friday at 11 p.m.
Police charged him with first-degree murder and first-degree burglary in the killing of Fannie Gumbinger, the Poughkeepsie Journal reported.
Gumbinger was found dead at her home early Wednesday morning, police said.
Relatives of the victim said they were relieved to hear of the arrest.
"At least we'll have some answers," Jacqueline Solomon, Gumbinger's niece, said.
Police declined to comment on a motive, and said Gumbinger died of multiple injuries.
Authorities said they will hold a press conference Monday to release more details of the case.
Rogers is also a suspect in multiple recent city burglaries, police told the Journal.