Lehman Brothers has agreed to sell its North American investment banking and capital markets businesses for $1.75bn to UK lender Barclays, which will use the acquisition to boost its US investment banking prowess without having to assume Lehman’s crippling liabilities.

The agreement comes after two days of around-the-clock negotiations between Barclays and Lehman, whose parent company filed for bankruptcy protection on Monday after a futile weekend effort to find a buyer for the entire firm.