The California Public Utilities Commission voted unanimously Thursday to initiate the investigation, which could take up to 18 months.
It will consider whether customers should continue paying rates for San Onofre and if they are due money back.
The vote came after dozens of residents and business leaders pleaded with the state utilities regulator against - and for - a plan to restart the plant, which has been offline since January.
A leak was initially discovered in one of the reactors' steam-generating tubes. Later, unusual wear was found in tubes in both reactors.
Southern California Edison, which owns 78 percent of the plant, said in a statement that the company will look to warranties and insurance to recover costs associated with the outages. Last year, the company estimated it would cost roughly $640 million to run the plant in 2012, said company spokeswoman Jennifer Manfre.
The Associated Press contributed to this report.