The office supply companies agreed to a $1.2 billion combination in February. The agency said its 7-month investigation showed that the combination isn't likely to cause competitive harm.
The companies said Friday that they expect the transaction to close on Tuesday.
Office Depot Inc., based in Boca Raton, Fla., runs more than 1,300 stores worldwide. OfficeMax of Inc. of Naperville, Ill., operates more than 900 stores in the U.S. and Mexico.
They each anticipate reporting their third-quarter earnings on Monday.
Office Depot's stock gained 21 cents, or 3.8 percent, to $5.80 in morning trading. Shares of OfficeMax rose 64 cents, or 4.3 percent, to $15.62.
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