Bader Ginsburg died on Friday at his home in Washington, as a result of pancreatic cancer.
"Our nation has lost a jurist of historical proportions.
We in the Supreme Court have lost a well-liked colleague.
Today we mourn, but with the firm conviction that future generations will remember Ruth Bader Ginsburg as we knew her - a tireless and resolute fighter for justice ", writes HD's Chief Justice John Roberts in a statement.
Bader Ginsburg has been treated for various forms of cancer several times over the years.
Last year, it emerged that she had undergone radiation therapy for a cancerous tumor in her pancreas.
Nominated by Clinton
She appeared in the Supreme Court in August 1993 after being nominated by Democratic President Bill Clinton. She was then the second woman after Sandra Day O'Connor to take her place in court and the first Jewish woman.