Shamir served as prime minister from 1983 to 1984 and from 1986 to 1992. His term was marked by the Palestinian uprising and the 1991 Gulf War, when Iraq fired 93 Scud missiles at Israel.
Israeli Prime Minister Benjamin Netanyahu said in a statement that Shamir "led Israel with a deep loyalty to the nation and to the land and to the eternal values of the Jewish people."
The White House praised Shamir for helping to forge strong ties with the U.S.
"Yitzhak Shamir dedicated his life to the State of Israel. From his days working for Israel's independence to his service as Prime Minister, he strengthened Israel's security and advanced the partnership between the United States and Israel," the statement said.
Barely over 5 feet (1.52 m) tall and built like a block of granite, he projected an image of uncompromising strength during the first intifada, or Palestinian uprising against Israel in the West Bank and Gaza.
Shamir was suffering from Alzheimer's disease and died in a nursing home on Saturday.
The Associated Press contributed to this report.