It was announced in February that the two companies were planning on merging, creating a $3bn (£1.9bn) printer.
However, the deal, which was supposed to complete in October, has dragged on, with more time given while the Federal Trade Commission (FTC) investigated the deal.
The FTC has now closed that investigation and no additional action is warranted at this time.
According to a statement from both companies: "RR Donnelley and Bowne expect to promptly complete the transaction, which remains subject to the satisfaction of other customary closing conditions."