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Lehman's has a combined near market value of $1.5 billion (£800m) and the deal is believed to be worth about $1.75 billion.
The deal, which is subject to approval by New York's bankruptcy court, would cover operations employing 10,000 people.
Robert Diamond, Barclays' president, said the deal was a once in a lifetime opportunity for the bank.
He commented: "We will now have the best team and most productive culture across the world's major financial markets, backed by the resources of an integrated universal bank."
Lehman Brothers chief operating officer Herbert McDade said the investment bank's strength is its client franchise.
In related news, the Qatar Investment Authority could increase its stake in Barclays, reports Reuters.
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