RALEIGH, N.C. — Duke Energy formalized deals Monday that ended separate investigations by North Carolina regulators and the attorney general into whether the utility misled officials before a merger that made it the country’s largest electric company.

The deals seek to balance greater oversight of the company with flexibility for its executives.

The North Carolina Utilities Commission voted unanimously to approve a settlement announced last week and negotiated by its staff and Duke Energy lawyers. The deal defines CEO Jim Rogers’ retirement at the end of 2013; sets the coming and going of several other executives and board members and requires the company acknowledge it has “fallen short of the commission’s understanding of Duke’s obligations” as a regulated utility.

Duke Energy sought to clear the air as it gears up to ask the regulator to approve two large rate increases in its largest market, said Dwight Allen, a Duke attorney. Duke Energy has 3.2 million customers in North Carolina and another 3.9 million in South Carolina, Ohio, Kentucky, Indiana and Florida.

“No doubt mutual respect and trust has been damaged,” Allen admitted to commissioners.

The commission had the power to reverse or change its earlier approval allowing the merger with in-state rival Progress Energy, which commissioners rushed to approve in late June to meet a deadline Duke and Progress set after federal regulatory delays.

Attorney General Roy Cooper’s office said Monday it is ending its probe with a separate settlement that seeks heightened consumer protection oversight of the company. Terms of the deal require the company to pay for independent satisfaction surveys of Duke’s North Carolina customers and up to 29,000 employees, then tell the attorney general how it will respond.

Duke Energy shocked investors and consumers just hours after the deal closed July 2 by firing Progress Energy CEO Bill Johnson, who for a year and a half had been promised the job heading the combined company.

The surprise CEO switch prompted shareholder lawsuits, led to consumers accusing the state regulator of being duped and drove down Duke Energy’s stock price more than 8 percent between the day before the deal closed and Thursday’s settlement announcement. Investors bid shares in the company 43 cents higher Monday to $64.25 by midday.

Duke also must come up with another $30 million for ratepayers and low-income assistance.

Analysts hailed the settlement negotiated by the company as good for Charlotte-based Duke Energy and its state regulator.

“The settlement resolves one of the major regulatory issues facing the company at a low financial cost and introduces a path for resolution of management succession issues,” Deutsche Bank Securities Inc. research analyst Jonathan Arnold wrote in a note to investors.

The settlement included several management reshuffles advancing former Progress Energy executives favored by regulators.