Graham Rawlinson died after Dhirendra Saha and Chulum Salim prescribed huge amounts of drugs, including the heroin substitute methadone.
Saha was jailed for 21 months and Salim for 12 months. They were ordered to pay pounds 10,000 each towards the pounds 50,000 costs of the six-week trial.
Sentencing them at Birmingham Crown Court, Judge Richard Curtis said: 'I am sure that each of you knew the properties of these drugs. The regime you promoted meant that the man in nine days had an enormous quantity, in total, of drugs.
'The regime caused his death since his heart and lungs were impaired, as you must have known they would be.'
He added that Saha received the longer sentence because he had prescribed the methadone.
'The worst thing was the addition of methadone on September 13 to the other drugs. Here, Dr Saha, you must take responsibility,' Judge Curtis said.
'I do not believe either of you could have properly examined Rawlinson. You each behaved with criminal recklessness totally unbefitting of the medical profession.'
The doctors, both aged 55 and GPs in Grimsby, prescribed the fatal cocktail as they worked as part- time police surgeons.
Salim, of Waltham, near Grimsby, and Saha of Grimsby, denied manslaughter.
Peter Birt QC, said that Rawlinson, 23, a former heroin addict, was transferred to Grimsby police station from Manchester's Strangeways prison in May 1990 after riots.
He was then prescribed the drugs cocktail by the two doctors, and changed from a 'fit, alert and cheerful young man' into a 'zombie-like figure'.
Mr Birt said Rawlinson was seen staggering, half-dazed with glazed eyes around the police station. When his girlfriend, Dianne McCarrick, phoned him his speech was slurred.
Within 10 days of arriving at Grimsby, he had slipped into a coma and was taken to hospital, the court was told. But after being discharged he was returned to the police cells, again slipped into a coma and died in September 1990.
The court was told that prisoners moved from Strangeways were given tranquillisers. Mr Birt said Rawlinson was given five times the maximum safe dose.
Defending Saha, Kiernan Coonan QC, said he was 'an extremely gentle person'.
'He received no guidance at all from anyone. He was overwhelmed by the demands of manipulative addicts.'
Robert Smith QC, for Salim, said: 'He has become depressed, withdrawn, anxious and tearful. The knowledge of what he was responsible for will remain with him for the rest of his life.'