BlackRock made its offer on Friday, and the new combined company will be the world's largest money manager with $2.8 trillion of client funds and will take the name BlackRock Global Investors.
Barclays said it would pay rival investment group CVC Capital Partners $175 million as compensation for exercising an option to reject CVC's earlier bid for BGI's iShares division, and invite its shareholders to approve the deal at a meeting in early August.
Barclays will gain much-needed capital from the sale to bolster its balance sheet, having earlier relied on support from Middle Eastern governments rather than Britain's to help it through the credit crunch.
BlackRock, founded 20 years ago as a bond investment firm, has managed to sidestep the toxic assets and vehicles that have laid low many competitors. The U.S. government selected BlackRock to manage troubled assets from Bear Stearns and American International Group Inc
The deal gives BlackRock exposure to exchange-traded funds, a product that has grown fast because it allows investors to buy assets easily that otherwise might be difficult to acquire, such as precious metals or foreign stocks.
(Reporting by David Milliken; Editing Bernard Orr)