The decision comes despite polls showing two-thirds of Japanese have serious concerns about nuclear plant safety after last year's earthquake and tsunami, The New York Times reported.
Noda announced the decision to restart the two reactors at the Ohi plant in western Japan after being informed by Fukui Gov. Issei Nishikawa that the prefecture would accept the restart of the Nos. 3 and 4 reactors at the plant, Kyodo News reported.
"Having won local consent, reactivating the Nos. 3 and 4 reactors of the Ohi nuclear power plant is now the government's final decision," Noda said. "We are determined to make further efforts to restore people's trust in nuclear policy and safety regulations."
Before the Fukushima plant was heavily damaged in March, about 50 commercial nuclear reactors were operating in Japan and they provided about a third of the country's energy supply.
Noda made an appeal on national television last week for the country to return to nuclear power to avoid electricity shortages that could cause blackouts and hurt industry.
On Friday, an anti-nuclear group led by the Nobel laureate Kenzaburo Oe gave the Noda government the signatures of 7.5 million people calling for the abolition of nuclear power.
Noda's government is backing a bill to create a more independent nuclear regulatory agency.