Dollar General bid $78.50 per share in cash, which is higher than Dollar Tree's offer of $74.50 per share in cash and stocks. Dollar Tree made the offer three weeks ago in what is being seen as a consolidation of the heated dollar-store segment.
Including debt, Dollar General's offer is valued at $9.7 billion and the company said it would pay the $305 million break-up fee Family Dollar would owe Dollar Tree for breaking the deal.
"For Family Dollar shareholders, our proposal is financially superior to the current transaction agreement with Dollar Tree and would provide Family Dollar shareholders with a substantial premium and immediate liquidity for their shares," said Rick Dreiling, Dollar General's chief executive officer.
Family General has been under pressure from activist investors to up the discount store's stock prices. Activist investor Carl Ichan, who disclosed his stake in the chain in June, and Nelson Peltz, who gained a seat on the board nearly three years ago after trying to buy the entire company, have been trying to up the store's value.
The combined company would have close to 20,000 stores and more than $28 billion in revenue, also giving Dollar General a wider store base, especially in rural markets. By comparison, Family Dollar's merger with Dollar Tree -- the smallest of the three -- would create a company with more than $18 billion in sales.
It was unclear if Dollar Tree would immediately up its offer and enter a bidding war with Dollar General.