Offering fresh evidence of the rapid consolidation among asset management firms, Legg Mason Inc. said Tuesday it has agreed to buy Brandywine Asset Management Inc. for about $135.3 million of stock.

The deal for the Wilmington, Del., company would boost by 13%, to $60 billion, the assets under management at Legg Mason, a Baltimore investment manager and securities brokerage. The transaction is slated to close in the first quarter.

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