MATTHEWS, N.C. — The battle for Family Dollar Stores Inc. is over, and the winner is the company with the less generous bid.

Family Dollar shareholders on January 22 voted to accept a cash-and-stock offer from Dollar Tree Inc. that valued Family Dollar at $8.7 billion at the time it was accepted.

The vote put an end to Dollar General Corp.’s competing bid of $80 a share, meaning that Family Dollar’s shareholders left about $400 million on the table when they followed management’s recommendation and spurned Dollar General’s offer. The Dollar Tree proposal won 89% of the vote.

While acknowledging that Dollar General’s offer was richer, Family Dollar chief executive officer Howard Levine and company directors asserted that it represented an unacceptable risk, given that the prognosis for regulatory approval was not good. Levine and others argued that antitrust regulators at the Federal Trade Commission were likely to demand significant divestitures or block the Dollar General deal outright rather than let the top two players in the dollar store market combine forces.

Both Dollar General and Family Dollar sell a broad mix of merchandise, typically for $10 or less, with roughly one-quarter of the items priced under $1. Dollar Tree, on the other hand, sells everything for a dollar or less, making a merger with Family Dollar less likely to lead to higher prices that would squeeze the families on a budget that shop at dollar stores for food and other necessities.

“By utilizing the $1 fixed price point in Dollar Tree and multi-price points in Family Dollar, we will deliver even greater value and choice to a broader range of consumers,” said Dollar Tree CEO Bob Sasser.

Dollar Tree’s proposed acquisition of Family Dollar remains subject to FTC approval. The companies say clearance could come as early as March.

Dollar General’s chairman and CEO, Rick Dreiling, characterized the vote to approve the union of Family Dollar and Dollar Tree as “a loss not only for Family Dollar shareholders but also for consumers across the country who will not have the opportunity to benefit from the cost savings and efficiencies that we believe would have been created by a merger between Dollar General and Family Dollar.”

Dreiling and other advocates of such a tie-up have asserted that the combination would serve as a counterweight to the influence of Walmart in an era when small-box stores are gaining favor with consumers seeking an easier, faster and more convenient shopping experience.

Despite the rebuff, Dollar General remains “well positioned for sustainable growth and shareholder-value creation,” said Dreiling, who also announced that he would remain Dollar General’s chairman and CEO for another year, unless a successor is appointed first.

The combination of Dollar Tree and Family Dollar will create a business with more than 13,000 stores in 48 states and five provinces in Canada, employing 145,000 people and generating $18 billion in annual sales. Dollar Tree and Family Dollar will continue to operate under separate banners once the deal is ­completed.