The concession, which had been widely expected, leaves a consortium led by Royal Bank of Scotland PLC in position to buy ABN Amro in a deal worth EUR70.5 billion (US$99.9 billion), the largest takeover in the history of the financial industry.
Specifically, Barclays said that fewer than 80 percent of shares had been tendered to its cash-and-share offer, worth EUR62.2 billion (US$88.1 billion), or EUR33.56 (US$47.53) per ABN Amro share at Barclays' current share price.
The mostly cash RBS bid, which closes Friday, is worth EUR38.04 (US$53.88) per ABN share - 13 percent more than the Barclays bid.
ABN's shares were flat at EUR37.71 (US$53.41).
Any shares that were tendered to the Barclays bid "will be deemed not to have been made," Barclays said in a statement. It added that it would demand a EUR200 million (US$280 million) breakup fee as a result of losing the takeover fight.
"This break fee will significantly exceed the costs that Barclays incurred" in launching its offer, the bank said.
ABN entered talks with Barclays in March and agreed to be acquired by the British bank in April, though it was forced to withdraw its support after RBS made its counterbid formal in July.
The RBS consortium has emerged ever more clearly as the favorite to buy ABN Amro Holding NV in recent weeks, as its bid was always worth more than Barclays, and it met various regulatory and fundraising hurdles.
At a shareholders' meeting on Sept. 20, ABN Amro Chief Executive Rijkman Groenink - who wanted Barclays to win - conceded that that was unlikely to happen.
"The market expects that the overwhelming majority of shareholders will chose for the consortium's bid," he said then.
Groenink had argued that the Barclays takeover was more consistent with ABN's own strategy and that the consortium bid was worth more but carried greater risks. He said it would amount to a "carve up" of ABN Amro.
Among the consortium, Fortis NV of Belgium wants ABN's Dutch operations, Banco Santander Central Hispano SA of Spain wants its Brazilian and Italian arms, and RBS wants the rest, including ABN's investment banking arm.
RBS's offer closes Friday afternoon, and it is expected to announce victory in the takeover fight, which began in March, on Monday. However, it will likely extend its offer for to allow holdout shareholders and those who tendered to Barclays to tender to the RBS bid.
The consortium persevered through major challenges in its quest to buy ABN, first when the Dutch bank sold its U.S. arm, LaSalle Bank Corp. of Chicago, to Bank of America Corp. for US$21 billion (EUR15 billion) in what was widely seen as a poison pill measure.
The move met legal challenges and was finally approved by the Dutch supreme court.
Many shareholders believed the consortium would be forced to revise its bid due to turmoil on global credit markets in September.
But the three banks never wavered and the last major hurdles were passed when Fortis - seen as the weakest link - successfully arranged funding for its end of the deal and received antitrust approval from the European Union this week.