The American firm makes oilfield equipment and, under the deal, it will become "the platform for oil and gas equipment solutions within Siemens."
The German firm said its $83-a-share bid had been unanimously supported by Dresser-Rand's board of directors.
Siemens is hopeful the transaction will be completed by next summer.
The acquisition is subject to approval by Dresser-Rand shareholders, as well as approval from regulators in Europe and the US.
The deal gives Siemens access to the US oil industry at a time when a drilling boom for oil in North America has led to higher demand for energy services and equipment.
Siemens - Europe's largest engineering company - "plans to operate Dresser-Rand as the company's oil and gas business retaining the Dresser-Rand brand name and its executive leadership team", a statement issued by Dresser-Rand says.
"In addition, Siemens intends to maintain a significant presence in Houston, which will be the headquarters location of the oil and gas business of Siemens."'Leveraging strengths'
In the statement, Lisa Davis, a member of the managing board of Siemens said: "Our aim is to become the leading rotating equipment and process system integrator for the oil and gas industry.
"Dresser-Rand has strong presence in oil and gas, a reputation for technology leadership and innovation, and a talented and experienced leadership team."
Dresser-Rand ranks among the world's largest suppliers of equipment to the global oil, gas, petrochemical and process industries.
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