By Shayndi Raice and Christopher Alessi

German engineering company Siemens AG announced a deal to acquire U.S. oil-equipment maker Dresser-Rand Group Inc. for $7.6 billion.

The Houston-based company is fetching $83 a share, in cash.

Dresser-Rand shares on Friday had shot up 9.4% to close at $79.91.

The German company beat out Swiss rival Sulzer AG, which had been in talks with Dresser-Rand over a stock-based merger, according to people familiar with the situation. The all-cash nature of the bid likely proved decisive in reaching a deal with the much smaller Dresser-Rand, analysts suggested. Siemens took in close to EUR76 billion ($97 billion) in revenue last year, while Dresser-Rand's total revenue was $3 billion.

Reuters reported on Sunday that Siemens was close to completing an agreement to acquire Dresser-Rand.

Morgan Stanley and Zaoui & Co. advised Dresser Rand, according to the company. Goldman Sachs and Deutsche Bank advised Siemens, according to people familiar with the matter.

The acquisition is in line with Siemens Chief Executive Joe Kaeser's aim of building up the company's presence in the U.S. energy market and capitalizing on the shale-gas boom.

Siemens produces gas turbines and supplies equipment for companies that extract natural gas. The merger with Dresser-Rand, which produces compressors, turbines and other rotating equipment, would allow Siemens to expand its gas-extraction capabilities and more directly profit from hydraulic fracturing in the U.S.

Siemens's large supply-chain network would enable it to harness Dresser-Rand's profitable business in spare parts and a "very high recurring stream of revenues," said Robert Norfleet, an analyst with Alembic Global who covers Dresser-Rand.

At the same time, analysts say Dresser-Rand is poised to benefit from growing demand for compressors for offshore oil-production platforms spurred by expansion of the U.S. energy industry.

Siemens is one of a number of German industrial companies, including chemicals groups BASF SE and Wacker Chemie AG, shifting to the U.S. energy market, in part because of Germany's strict controls over shale-gas exploration.

Mr. Kaeser in May appointed American Lisa Davis to head Siemens's power business, which is being led for the first time from the U.S.

Siemens in May bought most of Rolls-Royce Holdings PLC's civil energy operation for roughly $1.3 billion. The division has many customers in the oil-and-gas extraction industry.

In June, Siemens lost out to General Electric Co. on a bid for the energy assets of gas-turbine maker Alstom SA of France.

Siemens has also agreed with Robert Bosch GmbH to acquire Siemens's 50% stake in the joint venture BSH Bosch und Siemens Hausgeraete GmbH. The purchase price will total EUR3 billion. Siemens and Bosch will also each receive from BSH an additional distribution of EUR250 million before the transaction is completed. The transaction, which still requires regulatory approval, will probably be completed in the 2015 first half.

Write to Shayndi Raice at shayndi.raice@wsj.com

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