In the Pottermore article "Ministers for Magic" by J.K. Rowling, the years given for Cornelius Fudge's term are 1990 - 1996:
1990 - 1996
A career politician overly-fond of the old guard. Persistent denial of the continuing threat of Lord Voldemort ultimately cost him his job.
However, in Goblet of Fire Sirius explains that Crouch lost out on becoming minister to Fudge when his son died:
"So old Crouch lost it all, just when he thought he had it made," he continued, wiping his mouth with the back of his hand. "One moment, a hero, poised to become Minister for Magic... next, his son dead, his wife dead, the family name dishonoured, and, so I’ve heard since I escaped, a big drop in popularity. Once the boy had died, people started feeling a bit more sympathetic towards him, and started asking how a nice young lad from a good family had gone so badly astray. The conclusion was that his father never cared much for him. So Cornelius Fudge got the top job, and Crouch was shunted sideways into the Department of International Magical Cooperation."
This seems to indicate that Fudge became minister shortly after Crouch Jr. died. Earlier Sirius had said that Crouch Jr. died about a year after coming to Azkaban:
"No," said Sirius dully. "No, he’s not in there any more. He died about a year after they brought him in."
Voldemort was defeated in October of 1981. That leaves us about nine years until Fudge became minister according to J.K. Rowling. If we subtract the year that Crouch Jr. was in Azkaban, we have eight years.
When they come out of the Pensieve in Goblet of Fire Dumbledore tells Harry the following about the attack on the Longbottoms (the crime for which Crouch Jr. was imprisoned):
He and his wife were tortured for information about Voldemort's whereabouts after he lost his powers, as you heard.
"The attacks on them came after Voldemort's fall from power, just when everyone thought they were safe.
This seems to indicate that the crime was comitted shortly after Voldemort's downfall. Even if we give a full year for time between Voldemort's downfall and Crouch Jr.'s imprisonment, we still have about seven years until Fudge became minister.
How can the timeline be reconciled?