Maria Altmann, 89, has fought since 1998 to reclaim six Gustav Klimt paintings - including a colorful, gold-infused portrait of her aunt.
"I am feeling very good about the whole thing because it was dragging on and dragging on," Altmann said. "We are finally seeing an end, and I hope a happy end. I am very pleased that things can be solved in a friendly and peaceful way."
The two sides began mediation in March following the U.S. Supreme Court's decision last year that Altmann could sue the Austrian government.
Her attorney, E. Randol Schoenberg, said binding arbitration could begin as early as next month, and that a decision was expected in November.
"There are a lot of happy faces around the table today," said Martin Weiss, Counsel General for Austria. "It's an agreement all sides can view as fair."
The case stems from a 1998 Austrian law that required federal museums to review their holdings to see if they included works looted by the Nazis, and to find out whether the works were obtained by the museums without remuneration.
The Nazis seized the paintings from Altmann's Jewish family - including works that now hang in the Austrian Gallery - soon after they came to power in 1938.
Schoenberg says the family relinquished rights to the paintings in 1948 only in exchange for Austria's release of other art works that belonged to them.
Among the paintings, the gold-encrusted "Adele Bloch-Bauer I" is one of Klimt's most famous pieces, similar in style to the world renowned "The Kiss."
"It's literally priceless," said Jane Kallir, co-director of the Galerie St. Etienne in New York City, which introduced Klimt to the United States in 1959.
An estimated 600,000 works of art were stolen by the Nazis during Adolf Hitler's rule in Germany.
By Laura Wides