The verb headquarter occurs in both transitive and intransitive senses: The magazine has headquartered the reporters in a building that houses many foreign journalists. The European correspondent will headquarter in Paris. But this verb usage does not sit well with many people, and in an earlier survey a majority of the Usage Panel found both these examples unacceptable in formal writing.

Although there is a lot of evidence for these usages, you would do best to use alternative expressions, for example: The magazine has just assigned him to (or has stationed him in) a building that houses many foreign journalists. The European correspondent will make her headquarters in Paris (or will make Paris her headquarters).