LONDON — For the first time in the 116-year history of the Rhodes scholarship, students from anywhere in the world — even Britain — can now qualify for the award to study at Oxford University, the Rhodes Trust announced on Monday.

The news culminates a multiyear push by the trust to raise money from philanthropists, expand the number of scholarships and broaden the program — which until recently was limited to a fairly short list of countries — into something global. The result is far removed from the legacy of Cecil Rhodes, a South African diamond magnate and devoted British imperialist who saw the scholarships he endowed as very much an Anglo-Saxon and male privilege.

“If we believe in our mission to find incredibly talented people who will change the world for the better, they’re just as likely to be found in Indonesia as in Ohio,” said Charles R. Conn, the chief executive of the trust and warden of Rhodes House at Oxford. “We don’t feel constrained by who Rhodes was as a person, but perhaps each Rhodes scholar needs to reflect on that when they accept the money.”

When Rhodes died in 1902, he left instructions and money in his will for more than 50 students from a few current or former British possessions to study at Oxford, and five scholarships were soon allocated for German students. From the start, some scholarships were set aside for students from southern Africa, but for decades all of the recipients from those countries were white.