The offer is 9 percent above Bank's closing stock price Monday. Men's Wearhouse bid represents a premium to the one by Bank. The latter offered $48 per share in cash, or about $2.3 billion, for MW in Septemeber.
Shares in both companies jumped Tuesday.
"Following Jos. A. Bank's unsolicited public proposal to acquire Men's Wearhouse, our Board of Directors evaluated a number of alternatives to deliver value to our shareholders," Men's Wearhouse board's lead director, Bill Sechrest, said in a statement. "After a thorough review, our Board concluded that an acquisition of Jos. A. Bank by Men's Wearhouse has strategic logic and the potential to deliver substantial benefits to our respective shareholders, employees and customers."
After Bank's move, a large stakeholder in MW, Eminence Capital, urged that it be considered. In early November, Men's Wearhouse rejected Bank's bid, saying it significantly undervalued its business and was not in the best interests of shareholders.
(Read more: Jos. A. Bank terminates offer to buy Men's Wearhouse)
Following this rejection, Eminence sent a letter to Men's Wearhouse, urging it to review all strategic options, including a merger with Bank and a return of capital to shareholders. Shortly after this, Bank terminated its offer.
Stifel Nicolaus analysts said Tuesday that Men's Wearhouse shareholders would benefit from "improving purchase efficiencies, optimizing customer service and marketing practices, and streamlining corporate functions."
"Given that JOSB has previously stated it would be willing to be acquired by MW, we anticipate that JOSB will give MW's offer considerable consideration," they said.
—By CNBC's Katie Little. Follow her on Twitter