"Governments believed for a long time that opening the door to compensation would pose a threat to the very significant efforts made by France to have credible nuclear deterrent," Mr Morin told the newspaper, Le Figaro.
"But it was time for France to be true to its conscience," he added.
Mr Morin said that under the provisions contained in the proposed compensation bill, an independent committee of doctors led by a magistrate would examine those affected on a case-by-case basis.
Many of the 150,000 soldiers and civilians who witnessed the nuclear tests say they are suffering from diseases such as leukaemia and thyroid cancer.
Locals from Algeria and Polynesia who were at the tests will also be eligible
Crucially, our correspondent says, the burden of proof before the committee will not be on the victims to show that their illness is linked to the tests, but on the government to show that it is not.
Local people from Southern Algeria and Polynesia who were at the tests will also be eligible to apply for compensation.
"A first batch of 10 million euros has already been earmarked for the first year in the defence ministry budget," Mr Morin said.
The vice-president of the French Nuclear Veterans Association (AVEN) welcomed the announcement, but questioned how the government had arrived at the initial settlement of 10m euros.
"What's that figure based on? There's no medical follow-up. Out of 150,000 people who worked on the nuclear sites, how many are really ill?" asked Jean Luc Sans in a BBC interview.
"Ten million euros... that's just for show - it's a publicity coup."
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