For nearly 60 years the portrait of a baby-faced Philip IV by Velázquez hung in the Metropolitan Museum of Art’s European paintings galleries, a stunning example of the only 110 or so known canvases by that 17th-century Spanish master. Majestic in size, it was rare in its depiction of a young, uncertain monarch and was the earliest known portrait of Philip by Velázquez, who, as the king’s court painter, went on to record his image for decades.

So it was quite a shock when, in 1973, the Met, reconsidering 300 of its most treasured works, declared that the painting was not a Velázquez and was probably executed in his studio by an assistant or follower.

But in the museum world, 37 years is several lifetimes, especially considering how extraordinarily technology and scholarship have advanced. Now, after a year of examination and restoration, curators, conservators and scholars have changed their minds....