President Carter paid tribute to him as a "superb public servant".
One of his last tweets, sent in February, dryly noted: "Do we even have a foreign policy right now?"
"He played an essential role in all the key foreign policy events of my administration, including normalisation of relations with China, signing of the SALT II treaty [on arms control], brokering the Camp David Accords [on Middle East peace], and the Panama Canal treaties, among others," he wrote.
"He was brilliant, dedicated, and loyal, and remained a close adviser to my work at The Carter Center. I will miss him."
During the Iranian hostage crisis, Mr Brzezinski was also a leading force behind the failed US commando rescue mission, having come to believe negotiations would not work.
Mr Brzezinski (middle, with Jimmy Carter, second right) during the 1978 summit which resulted in the Camp David Accords
After President Carter lost to Ronald Regan in 1981, Mr Brzezinski turned to other things, including becoming a consultant on international affairs and a senior adviser for the Georgetown Center for Strategic and International Studies in Washington.
He also taught American foreign policy at Johns Hopkins University.
Sharing a picture of her father on Instagram, Ms Brzezinski, a journalist, wrote: "He was known to his friends as Zbig, to his grandchildren as Chief and to his wife as the enduring love of her life.
"I just knew him as the most inspiring, loving and devoted father any girl could ever have."