The move ends a decade-long legal battle, which began after it was discovered that the oil painting, "Portrait of Wally" by Egon Schiele, was loaned to New York's Museum of Modern Art in 1997.
The painting was seized by U.S. officials in 1999 and the United States began civil proceedings to return the painting to the estate of Bondi Jaray, who died in 1969. During legal proceedings, the Leopold Museum maintained the painting was not stolen from Jaray.
On Tuesday, the museum agreed to settle the case and pay Jaray's estate $19 million.
U.S. authorities had argued the painting was stolen from Jaray by a Nazi in 1939, returned to the Austrian government after the war and then ended up in the collection of Austrian collector Rudolph Leopold in the 1950s.
(Reporting by Michelle Nichols)