Last year, the Leopold Museum said it had agreed to pay $5 million in compensation to the sole granddaughter of Jenny Steiner, but that negotiations with two other sets of heirs continued.
"Following the settlement with the only living granddaughter of Jenny Steiner in May 2011, strenuous efforts have now led to another settlement with the heirs of Daisy Hellmann and Klara Mertens," the museum said in a statement on Thursday.
The board of directors of the Leopold Museum Private Foundation described it as a "long and hard-fought solution," the statement added. It did not give financial details.
The spat was one of at least two restitution cases the Leopold Museum had hoped to settle with funds raised by selling another Schiele painting, "Houses with Colourful Laundry, Suburb II", which fetched a record 24.7 million pounds ($38.5 million)at an auction in mid-2011.
The museum houses the world's largest collection of works by Schiele, one of the major Austrian artists of the 20th century.
"The painting 'Houses by the Sea' will as of now be accessible to the public as an integral part of the largest and most important Schiele collection in the world," it said.
Steiner, a Jewish silk factory owner and art collector, fled in 1938 when Nazi Germany annexed Austria and died in New York in 1958. Collector Josefine Ernst bought the painting at an auction in 1941. Her son sold it to Rudolf Leopold in 1955 to complement his collection of works by Schiele, the museum said.
Proceeds from the Leopold's sale of a Schiele cityscape at a Sotheby's auction in June last year were to be used to help pay for the settlement of another long-running dispute over a 1912 painting of Schiele's lover Walburga Neuzil.
A Manhattan court upheld claims that work had been seized by the Nazis, prompting the museum to pay $19 million in a settlement to keep it.
($1 = 0.6418 British pounds)
(Reporting by Fredrik Dahl, editing by Paul Casciato)