The BBC said the sale to an unidentified phone bidder set a record for the highest price paid for a drawing.
The work was a study for Raphael's "Transfiguration," which hangs in the Vatican Museum. The sketch was part of the private collection of the Duke of Devonshire, the British broadcaster said.
"If you are lucky, at some point in your career a work like this comes along," said Gregory Rubinstein, head of old master drawings at Sotheby's. "A number of the world's greatest collectors stepped up tonight in recognition of the genius of Raphael and the extraordinary beauty of this drawing, with its exceptional provenance."