And 17,000 civilians working for the Army will also be laid off, the official told AFP, confirming a report in the newspaper USA Today.
The paper quoted a document it had obtained and said the cuts are being made to save money.
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The cutbacks will affect virtually every Army post at home and abroad, USA Today said.
Under the plan the Army will have 4,50,000 soldiers at the end of the 2017 budget year, the paper said.
It added that in 2013 the Army argued in budgetary documents that going below 450,000 troops might mean it could not win a war.
By comparison, the Army swelled to 5,70,000 men and women during the peak of fighting in Iraq and Afghanistan, the paper said.
Across-the-board government budget cuts are due to kick in in October and if Congress does not avert these the Army will have to lay off another 30,000 soldiers on top of the 40,000, according to the document quoted by USA Today.
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