The price is 8% above URS' closing stock price of $52.02 on Friday, but 19% above the average price for the last 30 days. Shares spiked and retreated on Friday on a report that URS was looking to sell.
The California-based companies said the combination was necessary to build an integrated infrastructure services company that can operate globally and provide services including design, financing, construction and operation of buildings. The combined firm will have its headquarters in Los Angeles.
The companies had worked together on projects such as the Barclays Center in Brooklyn and the World Trade Center in New York.
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Aecom CEO Michael Burke said the deal will give Aecom a broader portfolio of services and access to URS' strong client relationships in the oil and gas, power and government services sectors.
The offer includes $33 per share in cash and 0.734 Aecom shares for every URS share.
URS CEO Martin Koffel said in a conference call the deal gives its shareholders "a right on the future as well as a cash takeout."
Shareholders can elect to receive all cash or all stock, although stock proceeds are expected to be tax-free, the companies said.
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Aecom expects annual cost savings of $250 million by the end of the fiscal year through September 2016. The deal is expected to boost per-share net income in the year through September 2015.