The decision in Washington by the IMF's 24-member board of member countries was made in two stages and included a secret straw poll followed by a formal vote.
Board officials, speaking on condition of anonymity, said it was obvious going into Friday's vote that Strauss-Kahn held a clear majority over Russia's nominee, former Czech Prime Minister and central bank governor, Josef Tosovsky.
Strauss-Kahn will begin his five-year term on Nov. 1, succeeding Spaniard Rodrigo Rato, who announced in July he would step down after the IMF's fall meeting in mid-October.
"The executive board of the International Monetary Fund has just chosen me to succeed Rodrigo de Rato as managing director," Strauss-Kahn said in a statement. "This is for me a joy, honor and responsibility," he added.
A European has led the global financial institution since its post-World War Two inception in 1945. But the IMF's legitimacy has been questioned by the world's emerging economic powers, which want a greater say in the fund's decisions and economic policy advice.
Once at the center of financial crises in Asia and Latin America, the IMF's role has recently changed amid global economic calm where there has been less need for its emergency loans.
Since the crises, rapidly-growing emerging economic, especially in Asia, have amassed huge international reserves with many countries pooling the funds in regional agreements, which would mean they won't need to turn to the IMF for aid during future crises.