The surprising announcement that AT&T Inc. would acquire T-Mobile USA from Deutsche Telekom AG in a $39 billion merger leaves one giant question mark: Will the U.S. government approve an acquisition that most experts thought was unthinkable until recently?

At the very least, most technology, finance and policy experts say the combination of the second and fourth largest providers of U.S wireless service by revenue will face a rocky road as the two companies seek approval from government regulators.

First, AT&T will need the FCC's approval to acquire T-Mobile's spectrum licenses.

But the deal is also certain to face a thorough investigation by the Justice Department, according to people familiar with the matter.

The merger is likely to be of particular concern to antitrust enforcers because the industry's two dominant companies—Verizon Wireless, a joint venture of Vodafone Group PLC and Verizon Communications Inc., and AT&T—are already so far ahead of anyone else, raising the specter of an effective duopoly in mobile telephony.