In an interview with Le Figaro newspaper earlier this year, Morin said some 150,000 people - including civilian and military personnel - were on site for the 210 tests France carried out in the Sahara Desert and the South Pacific from 1960-1996.
Compensation will be decided on a case-by-case basis.
Victims are to submit a claim to a committee made up of seven representatives of the state and two members from outside the government, which will make a recommendation to the defence ministry. The ministry will then notify victims of its decision.
Morin has said that anyone with health problems who resided near the test sites would be eligible to seek payouts under the bill - including Algerians, whose country won independence from France in 1962, after the nuclear test programme had started.
Size of the problem
No Algerian or French Polynesian victims associations have responded to Al Jazeera's request for reaction to the new law.
However, Algerian victims of French nuclear tests have sought compensation for years.
The head of the victims' organisation, Sahara Mohamed Abdelhak Bendjebbar - claiming the tests affected some 30,000 Algerian nationals - took the issue to the International Court of Justice in 2007.
Algerian scientists contend that France carried out 17 nuclear tests in the Sahara desert between 1960 and the final withdrawal of French troops from the region in 1967.