Duke offered $60 in cash for each Piedmont share, representing a premium of about 42 percent premium to the stock's Friday close.
Piedmont's shares were trading up 8.5 percent at $45.81 in light volumes premarket on Monday. (Get the latest quote here.)
A glut of supply from shale fields has ensured relatively stable pricing for natural gas distributors such as Piedmont.
This has prompted a number of U.S. power producers to boost their natural gas infrastructure and lower dependence on power generation at time when demand for electricity is weakening due to increased energy efficiency.
Duke and Piedmont are also partners in the $5 billion 550-mile (885-km) Atlantic Coast pipeline, which moves gas from Pennsylvania's Marcellus shale field to North Carolina and Virginia.
Duke will also assume about $1.8 billion of Piedmont's net debt, giving the company an enterprise value of $6.7 billion.