Police are still searching for the missing head and lower legs.
The dead woman was identified as Liu Hong Mei, a 22-year-old Chinese national who worked in Singapore as a production operator, a police statement said, noting that the victim's family had already been informed.
The suspect will be charged on Saturday, it said.
On Thursday, a cleaner found one box containing the lower torso on the banks of the Kallang River near Crawford Street, just outside Singapore's central business district.
Police later found the other box containing a headless upper torso with arms attached.