The Court of Appeal is expected to announce the award on Friday.
It follows years of legal action against British Coal in connection with Vibration White Finger injury.
Because British Coal closed at the end of last year, the government will take on liability for the compensation award.
The miners' lawyer Andrew Tucker said: "It has been a long war and this is the last battle, I hope."
He said he had been in negotiation with the Department of Trade and Industry since a High Court ruling last September that British Coal had been negligent in failing to protect its employees from the harmful effects of vibration since 1975.
Highest award
He said the highest award for an individual miner would be around £15,000 and the lowest would be £2,000 to £3,000.
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If miners had also suffered financial loss as a result of injury, the award could go higher. Awards would depend on the severity of injury.
Vibration White Finger, a form of the condition Raynauds Phenomenon, restricts blood supply to the fingers and is particularly triggered by the cold.
It is caused by vibrating tools, such as drills.
It begins with numbness and tingling sensations and can lead to disabling pain and whitening of the fingers.
Rapid conclusion
Belddyn Hancock of the Pit Deputies' Union said: "I am delighted that we have once again beaten the govenment in the courts on this vitally importnat issue for mine workers."
He urged all miners affected to contact their trade unions and lawyers to find out about compensation.
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He accused the government of trying to use the Court of Appeal to cut compensation awards.
"The government's attempt to have damages reduced has failed miserably," he said and called for government officials to sit down with miners' sollicitors to "thrash out a fair scheme" for compensation as soon as possible.
The Department of Trade and Industry denied it had sought to reduce compensation levels and said it had just sought "clarification" of the High Court ruling.
It expects to offer interim payments of £1,000 to around 3,000 miners with evidence of severe injury over the next few weeks.
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Energy minister John Battle said: "The government is keen to bring these discussions to a conclusion as rapidly as possible."
He added: "I fully sympathise with the many ex-miners who are suffering and have suffered for far too long, which is why it is imperative we do all we can to agree arrangements rapidly with the solicitors representing the plaintiffs so that we can begin settling valid claims."
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