Rahman took about £4,800 from his victims, telling them the money would be used to rehome the animals, the court heard.
But he actually left the pets to suffer and did not keep in touch with the families to update them on their progress, as he had promised.
Judge Richard Conley said: “[The] gravity of the offending is so great… I can barely conceive of a more serious offence of this type.
“No sentence that I can lawfully impose can adequately reflect the justifiable anger and disgust at what you have done.”
Twenty-one live dogs and a cat were found in small and dirty spaces, living without water, food or decent living conditions.
Three of the dogs were so unwell they had to be put down, and one poodle later went blind, the court heard.
Police found 37 dead dogs when they first searched the rehoming centre, where dogs were left to roam among the carcasses.
Four more dead dogs were found when a shed was demolished during a later visit.