The 39-year-old man will appear at Dundee Sheriff Court on Monday after the gruesome find in the Angus town’s Market Street late on Wednesday night.
Reports suggest parts of the body were found in bins outside the flat.
A major investigation was launched on Thursday, with Market Street and neighbouring John Street sealed off as forensic examiners in white suits carried out a detailed probe.
A recycling centre around one mile away on the town’s Bloomfield Road was also closed and sealed off by police as part of the investigation.
Senior officers said the incident is a “contained matter” and that a “complex investigation of a number of properties” would continue.
Police earlier said the body parts were found when they went looking for a person who had been reported missing.
Shocked locals reacted with horror at the news of the find.
Bed and breakfast owner Kate Andrew said she woke to find her rubbish bins sealed off with police tape on the pavement outside her home.
She said: “I got a message from a friend asking what was going on in my street and I hadn’t a clue.
“It’s really quiet here and a nice area.”
Detective Superintendent David McLaren said: “There will be a large police presence in the area for some time as we continue with the complex investigation at a number of properties.
“This is an extremely unusual incident and I would like to reassure the public that it is contained matter.
“A man has now been charged and is expected to appear in court on Monday.
“At this stage formal identification of the deceased has not been done and further information will be released in due course.”