Jim R. Bounds/Bloomberg News

Duke Energy, a big power company based in North Carolina, said on Monday that it had agreed to acquire a rival, Progress Energy, in an all-stock deal valued at $13.7 billion, creating the nation’s largest utility company. The combined company would have $22.7 billion in annual revenue and more than seven million customers in North Carolina, South Carolina, Florida, Indiana, Kentucky and Ohio.

The boards of both companies unanimously approved the deal, which is expected to increase profit in the first year.

“Our industry is entering a building phase where we must invest in an array of new technologies to reduce our environmental footprints and become more efficient,” James E. Rogers, the chief executive of Duke Energy, said in a statement. “By merging our companies, we can do that more economically for our customers, improve shareholder value and continue to grow.”

Duke agreed to pay $47.48 a share for Progress, a premium of 6.4 percent over the average closing share price of Progress Energy in the 20 days through Friday.

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Shares in Progress have risen more than 3 percent since DealReporter, a publication owned by The Financial Times, first reported on potential deal talks on Thursday. The company’s stock closed at $44.72 on Friday and slipped 73 cents, to $43.99 a share, on Monday. Stock in Duke, which is based in Charlotte, N.C., fell 21 cents, to $17.58 a share.

It is the latest in a wave of utility deals as companies seek to cut costs and combat falling prices by increasing their customer bases. Energy and power deals made up the biggest share of merger activity in 2010, accounting for 20 percent of announced takeovers, based on Thomson Reuters data.

Duke bought Cinergy of Ohio in 2005 in a $9 billion all-stock deal.The companies hope to complete the deal by the end of 2011. Several regulators will have to sign off, including the Federal Energy Regulatory Commission, the Nuclear Regulatory Commission and two state authorities.

The merger could advance the companies’ nuclear ambitions.

In 2007, Duke applied for permission to build a nuclear plant with two reactors in Cherokee County, S.C., called William States Lee III. Progress Energy has proposed building two reactors adjacent to its operations near Raleigh, N.C., and two more at a new site in Levy County, Fla.

But the companies have yet to make any real progress on the projects. None of the three projects are in line for government loan guarantees, and in the current economic environment, none are a sure thing.

One reason is the cost of the projects relative to the companies’ balance sheets. A two-unit plant can run upward of $8 billion, representing about 14 percent of Duke’s total assets.

Neither the Levy nor Lee project “was going to go forward unless Duke or Progress found partners that were willing to come in,” said John J. Reed, chief executive of an energy consulting firm, Concentric Energy Advisors, in Marlborough, Mass., who specializes in nuclear energy. The merger provides “a ready-made partner,” he said.

A tie-up might even speed up the timeline on some nuclear projects, said Edward D. Kee, a vice president of NERA Economic Consulting and a specialist on the finances of the new reactor market. By merging, they may be able to build one plant in 2015, instead of 2020, he estimated.

If the deal is cleared, Mr. Rogers is expected to become executive chairman, a role in which he would advise the chief executive on strategy and be the company’s main voice on energy policy.

William D. Johnson, the chief executive of Progress Energy would become president and chief executive of the newly formed company, to be called Duke Energy.

“This combination of two outstanding companies is a natural fit,” Mr. Johnson said in a statement. “It makes clear strategic sense and creates exceptional value for our shareholders.”

Duke was advised by JPMorgan Chase, Bank of America Merrill Lynch and the law firm Wachtell, Lipton, Rosen & Katz. Progress was advised by Lazard, Barclays Capital and the law firm Hunton & Williams.