"globally influential" is correct and usable in written English.
You can use it when you are talking about something that has influence and reach across the world. For example, "Disney is a globally influential company."
The result has been globally influential.
Nudge became one of the most globally influential ideas among policymakers.
Having won a Seed award in 2005, Blue Ventures has gone on to become a globally influential community conservation programme.
Mexico: A Revolution in Art, 1910-1940 When did the art of the Americas first become globally influential?
Too many people think they already know all they need to know about this shadowy fraternity, which remains globally influential.
This weeklong festival, which runs from June 23 to 29, 2014, will feature iconic works from Palestinian cinema, which has emerged as a globally influential artistic force.
With Tokyo becoming globally more influential in fashion, the question begs: "What is the difference between California style and Tokyo fashion?" "In Tokyo, everyone is into fashion," Takagi says.
Early projects in Baltimore, Boston, and Toronto were influential globally, although strict replication did not work well in other countries and cultures.
But he did not know that, halfway around the world, chefs like René Redzepi, Magnus Nilsson and Mathias Dahlgren in Scandinavia were doing similar research and developing the cuisine that has become hugely influential globally at restaurants like Noma, Relae and Faviken — and now at United States restaurants like Acme and Frej in New York, and Plaj in San Francisco.
If salsa is today a globally popular and influential dance music style, that is due in no small part to "Our Latin Thing," which documents a concert by the Fania All-Stars at the Cheetah club on 52nd Street in Manhattan on Aug. 26, 1971, and the chain of events it set in motion.
The service was attended by chefs dressed in their working whites who had travelled from as far afield as Japan to pay their respects to France's most globally celebrated and influential chef, the man who in 1975 created black truffle soup, named after President Valerie Giscard d'Estaing.
