WASHINGTON—Americans should be able to take their used cellphones and tablets freely from one wireless carrier to another if they aren't under contract, the White House said Monday, offering the latest victory to Internet activists seeking to shape U.S. technology policy.

Wireless companies have long sold cellphones at discounted prices in exchange for long-term service agreements. The catch: Consumers can't easily take what would otherwise be an expensive smartphone to a rival carrier who offers a better price while the phone...