The proposed sale will create a company with combined assets of over $2.7 trillion - or roughly the equivalent of the UK's annual economic output, the BBC said.
Under the terms of the agreement, BGI staff who own shares in the firm will receive a windfall payment. BGI president Bob Diamond is set to pocket Â£16 million.
Meanwhile Barclays, which will retain a 19.9 percent stake in BGI, will receive a fresh injection of capital to further insulate itself from losses on toxic loans and assets, BBC business editor Robert Peston noted.
The move means the bank will cancel an earlier agreement to sell BGI's exchange-traded fund specialist iShares to CVC Partners for $4.4 billion.
Barclays will pay CVC $175 million to break the deal, unless CVC submits an offer for the whole of BGI, in which case a bidding war would ensue.