The 9 1/2-inch-by-6 1/2-inch painting will hang in the Rembrandt House Museum in Amsterdam through June 29, on loan from the anonymous Briton who bought it at the auction by Moore, Allen and Innocent in Gloucestershire and had it cleaned and examined by British experts.
Art expert Jan Six from another auction house, Sotheby's, declined to put a new value on the painting. But he said the sale itself was a rare opportunity, as Rembrandt's works come on the market only once every few years.
"A self-portrait by Rembrandt, that's absolutely unique — not in my lifetime," Six said.
Rembrandt made the self-portrait about 1628, when he was in his early 20s and still in his hometown, Leiden. Already he was earning his reputation as an artist, and experimenting with a mirror and his own face to capture expressions.
"It has an incredible presence," said Ernst van de Wetering, head of the Rembrandt Research Project and an authority on the Dutch master. "The light has the most natural quality of light you can think of. ... and I love the naturalness of the laughing."
The painting previously had been in the hands of an English family for more than 100 years, according to Moore, Allen and Innocent. Some had assumed it to be by one of Rembrandt's students or a Rembrandt imitator.