The French Polynesian president Edouard Fritch has hailed as historic the French decision to remove the term negligible risk from the nuclear compensation law.
The National Assembly unanimously voted to amend the law, drawn up by Herve Morin when he was the defence minister in 2009.
Most claims for compensation for ill health because of the weapons tests have been rejected which prompted sustained calls for the law to be amended.
Mr Fritch said the Assembly decision marks a historic day and a relief.
He has hailed the territory's parliamentarians in Paris for their work and praised the tireless efforts of the nuclear test veterans organisations and the Maohi Protestant Church.
On Tuesday, the Senate is expected to also approve the amendment.
France tested its atomic weapons first in Algeria and then from 1966 to 1996 in the South Pacific in a programme which involved more than 100,000 personnel.