Dresser-Rand's board of directors has unanimously recommended the $83 per common share cash offer to shareholders - a 3.8 percent premium to Friday's closing price of $79.91, which had already been bolstered by takeover speculation over the past week.
Dresser-Rand had revenue of $3.03 billion in 2013 and net income of $168 million.
Siemens expects the transaction to close by the summer of 2015.
Siemens has trumped a competing offer from Swiss pump maker Sulzer AG, which said last week it was discussing a potential stock-based merger with Dresser-Rand.
Separately, Siemens announced the sale of its 50 percent stake in BSH Bosch und Siemens Hausgeraete to joint venture partner Robert Bosch for 3 billion euros (around $3.85 billion).