Albright was a tough-talking diplomat in an administration that hesitated to involve itself in the two biggest foreign policy crises of the 1990s - the genocides in Rwanda and Bosnia-Herzegovina.
"We are heartbroken to announce that Dr Madeleine K. Albright, the 64th U.S. Secretary of State and the first woman to hold that position, passed away earlier today. The cause was cancer," the family said on Twitter.
Albright was U.S. ambassador to the United Nations from 1993 to 1997 and U.S. President Bill Clinton's secretary of state from 1997 to 2001.
Born Marie Jana Korbelova in Prague on May 15, 1937, her family fled in 1939 to London when Germany occupied Czechoslovakia. She attended school in Switzerland at age 10 and adopted the name Madeleine.
Albright attended Wellesley College in Massachusetts and got a doctorate from Columbia University. She became fluent or close to it in six languages including Czech, French, Polish and Russian as well as English.
She was nominated to become the first woman secretary of state and confirmed unanimously in 1997. She was in the post until 2001.
While at the United Nations, she pressed for a tougher line against the Serbs in Bosnia after Bosnian Serb military forces laid siege to the capital Sarajevo.
During efforts to press North Korea to end its nuclear weapons program, which was eventually unsuccessful, Albright travelled to Pyongyang in 2000 to meet North Korean leader Kim Jong-il, becoming the highest-ranking U.S. official to visit the secretive Communist-run country.
Once the Clinton years and the 1990s were over, Albright became an icon to a generation of young women looking for inspiration in their quest for opportunity and respect in the workplace. Albright was fond of saying: "There's a special place in hell for women who don't help each other.