The Pentagon awarded Boeing Co. a contract worth more than $30 billion for aerial refueling tankers, closing a chapter in a tortured bidding contest, but potentially launching a fresh trans-Atlantic political controversy.

The award preserves Boeing's decades-long position as supplier of refueling aircraft to the Air Force, and shores up its standing as a U.S. national champion. The Pentagon's move is also likely to feed perceptions in European capitals that the U.S. defense market—the biggest in the world—remains largely...