The victim in the "jigsaw" murder case was a 49-year-old white British man, police have said.
Detectives released further details about his identity as they continued to question a man and a woman in connection with his murder.
The inquiry was launched last month after a man's left leg with the foot attached was found in a lay-by at Cottered, Hertfordshire before his head, torso, arms and right leg were discovered at separate rural locations in Hertfordshire and Leicestershire.
Only his hands are still missing but officers now believe they know the identity of the victim of the gruesome and possibly gangland crime.
The breakthrough came after a member of the public called detectives in the incident room about a missing person following a number of police media appeals to try to identify the victim.
Bedfordshire and Hertfordshire Major Crime Unit said a man aged 37 and a 20-year-old woman were arrested on suspicion of murder at an address in Southgate, north London, on Tuesday afternoon.
Earlier, magistrates gave detectives until Friday afternoon to question the pair, who are being interviewed at a police station in Hertfordshire.
The victim is expected to be identified publicly once a DNA test has been carried out.
Detective Chief Inspector Michael Hanlon said: "Extensive work has been carried out in relation to this murder investigation and I can confirm that two people have been arrested on suspicion of murder.
"We believe we have identified the victim of the murder and specialist officers are currently working closely with the family."