He said his painting would “fit perfectly” into the Prado, home to a vast collection of Velázquez paintings and other Spanish masterworks. The museum plans to hang it next spring and called it “a long-term deposit” by Mr. Jordan. The donation also coincides with the recent start of a nonprofit organization, American Friends of the Prado Museum, that the museum hopes will aid its ties and profile in the United States.

Mr. Jordan acquired the painting in London at an auction of Phillips, where it was mistakenly labeled, both in terms of its subject matter and author. While the work ostensibly represented Don Rodrigo Calderón, “it was very obvious to me that it was” King Philip III, Mr. Jordan said. The work was also wrongly auctioned as painted by somebody from the circle of Justus Sustermans, a Flemish painter. Mr. Jordan also initially made a wrong assumption that the portrait was a fragment of a larger painting rather than a preparatory oil sketch.

The Prado estimated that the work was done between 1623, when Velázquez introduced a new style of royal portrait, and 1631, when he returned from a stint in Italy and again significantly changed his portrait style. The fact that Philip III is shown in profile, looking up, fits with descriptions of how the king was portrayed in “The Expulsion of the Moriscos.”

Mr. Jordan, 76, is considered a specialist on Spanish art, but he called his personal collection “eclectic” and said that it included a sizable amount of French drawings from the 19th century. He said that he had not made plans to donate more of his works.

He also would not discuss the estimated worth of the donated Velázquez, even though it has been valued for tax purposes. The painting was historically important, a precursor to one of the major lost works of the artist, but “this is not a trophy Velázquez,” Mr. Jordan said. “It is something that he did for himself in the process of producing a very important work.”