All four were found guilty of plotting to overthrow the country's military junta and have been informed of the Supreme Court's decision.
"Their appeal has been rejected and the only recourse for them is to wait for a pardon from Than Shwe," a source close to the family of the former dictator said.
Another legal source confirmed that a full bench of the highest court had heard and rejected their appeal.
"The legal procedures they can take are finished now. This is the final step," the source added.
The son-in-law and three grandsons of Ne Win were sentenced to death by hanging last September by a lower court, after being arrested on charges of attempting to instigate sections of the army against the ruling junta.
"Their appeal has been rejected and the only recourse for them is to wait for a pardon from Than Shwe"
Friend of Ne Win's family
Their first appeal to the court, heard by two judges was rejected. They thereafter were allowed to appeal once more before a full five-member bench.
But diplomats said they were unlikely to be hanged, as the death penalty has not been used by the military, since it assumed power in 1988.
The once all powerful Ne Win family's fall has been remarkable.
Ne Win died last December in his Yangon home, where he had been under house arrest since March. He had ruled the country with an iron-hand for quarter-century, finally stepping down in 1988.
Many of his relations had grown disgruntled at having lost their economic and political privileges as Ne Win's power diminished.