Noda gave the restart order Saturday shortly after Oi Gov. Issei Nishikawa announced his acceptance of the restart. The reactors could be generating power within the next two weeks, officials said.
Last month the last of Japan's active reactors was shut down, marking the first time the country was without nuclear power in four decades.
"We are determined to make further efforts to restore people's trust in nuclear policy and safety regulations," Noda said Saturday.
But the restarts come amid division among Japanese about the safety of nuclear power since the Fukushima power plant disaster following the March 11, 2011, earthquake and tsunami.
A recent Pew Research Center poll indicates 70 percent of Japanese surveyed want nuclear power reduced or eliminated, with 80 percent of respondents saying they disapproved of the government's response to the Fukushima nuclear crisis.
An editorial in Tokyo Shimbun last Friday questioned Saturday's inevitable approval: "Does this reflect the sentiment of the citizens, who are seeking an exit from nuclear power? Won't it instead make what was supposed to be a rare exception par for the course?"
Also Friday an antinuclear group led by the Nobel Literature laureate Kenzaburo Oe presented the Japanese government with what it said was the signatures of 7.5 million people calling for the abolition of nuclear power.
Kansai Electric Power Co., operator of the Oi nuclear plant, had said that without the restarts, the demand for electricity this summer would exceed supply by about 15 percent. The reactors are expected to reach full operation late July.
The fate of Japan's 48 other reactors remains in limbo.
The Japanese government is slated this summer to devise the country's new energy strategy, which could shape the future role of nuclear power.
Last Thursday major Japanese political parties agreed on a bill to establish a new nuclear watchdog that would replace the scheme of government, industry and regulators whose interdependence has been blamed for lax safety standards.
The bill is expected to be passed by the Upper House this week. Even so, the new regulatory commission wouldn't take the reins from the current troika before September.
As far as future reactor restarts, an unnamed government official in charge of establishing the new commission told the Yomiuri Shimbun, "If we hasten procedures [on reactor restarts], the public's confidence in the new regulatory commission will be lost."
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees