'has been migrating' is correct and usable in written English.
You can use it to describe a process of movement that has been occurring over a period of time. For example: The population of emperor penguins has been migrating further south over the past few decades in order to find suitable cold habitats.
Regardless of personal style, top-flight talent has been migrating to hedge funds and private equity for years.
As Mr. Grede of Industrie noted, "a substantial part of the global readership has been migrating online".
After all, cutting-edge contemporary architecture by the likes of Libeskind and Foster has been migrating steadily into the cultural mainstream for years.
Actual political might has been migrating away from the parties, never mind the people who go to parties, more rapidly than ever.
His wife, Rachel, and their ever-expanding family would join him on those long trips north, including his daughter Minerva, an American citizen who says she has been migrating "since I was born".
Over the last two weeks, a treacherous and incurable plant disease called citrus canker that began showing up in backyards five years ago has been migrating into commercial groves in South Florida, threatening the state's $8.5 billion citrus fruit industry.
Now Fay tells me that the name has been changed, and the website has been migrated over.
The purpose is to check whether the destination host remains not overloaded after the VM has been migrated.
Farago says the Trestle platform has been migrated to Flurry's infrastructure, so that AppCloud can "support any sized app audience to enormous scale".
Compared to ANTARES, more functionality has been migrated to the shore, thus allowing for timely deployment of the telescope components and easy access to the system during the long lifetime of neutrino telescopes.
Professor Zolberg resists the term "age of migration" (coined by the scholars Stephen Castles and Mark J. Miller) because people have been migrating since the beginning of time.
