Taro Aso signed the agreement after attending a ceremony commemorating the 64th anniversary of the Hiroshima bombing, the Kyodo News Service reported.
The agreement certifies plaintiffs who won district court level lawsuits as victims even if their cases have not gone to higher courts.
"Considering that the plaintiffs are aging and they have fought this legal battle so long, we have decided to introduce the new policies to bring relief to them swiftly by paying respect to the legal decision," Aso said.
He initiated the agreement after the government lost 19 lawsuits.
"The government solemnly acknowledges the fact that stern judicial decisions have been given on 19 occasions over the certification of atomic bomb-related illnesses," Chief Cabinet Secretary Takeo Kawamura told reporters.