The deal would make Hitachi the world's largest power grid company, local media said.
Under the plan, ABB will spin off its power grid unit, for which Hitachi will buy an 80.1 percent stake for 704 billion yen in early 2020, the Japanes company said in a statement.
"We plan to buy the remaining shares so that Hitachi can make the unit its wholly owned company,” a spokesman said without disclosing how much that would cost.
ABB's power grid unit makes and operates infrastructure including power transmission equipment and control systems in numerous countries.
The deal would also make Hitachi the world's second-largest heavy electrical equipment maker by revenue, behind only General Electric, according to local media.
The Nikkei business daily first reported the planned deal last Thursday, but Hitachi shares have since dropped 2.5 percent.
Ratings agency Standard & Poor's said the power transmission and distribution business is growing globally, with service solutions a particularly promising field.
But "the business' profitability can be volatile, depending on how well a company manages projects related to equipment delivery”, it added.
ABB was created in 1988 as a result of the merger of Swedish-founded ASEA and Swiss BBC. Today it is headquartered in Zurich, Switzerland.