Michael Spalding's body was found in a suitcase by men working near Icknield Port Road on 12 May, police said.
Lorenzo Simon, 34, was found guilty of murder last week and was jailed for at least 19 years.
His partner Michelle Bird admitted assisting an offender and was jailed for two and a half years.
She was cleared of murder following a five-week trial at Birmingham Crown Court.
West Midlands Police said Mr Spalding, 39, who was the defendants' tenant, was treated as "slave labour", and forced to renovate their flat on Oxford Road, Smethwick.
A row prompted by a car accident led to Mr Spalding's murder at the flat, officers believe.
Police said he was killed in a "brutal" assault, before being dismembered with a variety of tools and stuffed into two suitcases, which were then thrown into the canal, weighed down with broken slabs.
One suitcase was recovered by contractors working for the Canal and River Trust, while a second was later found by police on the canal bed, along with a hacksaw.
The black suitcase containing the victim's torso was first spotted on 5 May floating in the water near Pope Bridge by a narrow boat owner, police said.
Eight days later the contractor, suspecting the case contained a dead animal, towed it to the bank.
Police said Simon moved to Derby when news of the body find broke but was arrested with Bird on 19 May.
Detectives later heard accounts from neighbours in Oxford Road who told of "aggressive, nasty" arguments coming from the flat.
A man has been jailed for life for murdering his friend before dismembering his body and disposing of it in a Birmingham canal.