Mr Powell's family said in a post on his Facebook page: "He was fully vaccinated. We want to thank the medical staff at Walter Reed National Medical Center for their caring treatment. We have lost a remarkable and loving husband, father, grandfather and a great American."
As a four-star Army general, he was chairman of the military's Joint Chiefs of Staff under President George H.W. Bush during the 1991 Gulf War in which U.S.-led forces expelled Iraqi troops from neighbouring Kuwait.
Mr Powell, a moderate Republican and a pragmatist, later served as secretary of state under President George W. Bush.
In response to the death, Piers Morgan has tweeted: "General Colin Powell, 84, has died from complications from COVID-19.
"He was an outstanding military leader & war hero and the first Black US Secretary of State.
"He was also a highly intelligent, courageous, charismatic and decent man.
"Very sad news."
Mr Powell oversaw Operation Desert Storm during the first Gulf war.
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Tributes have flooded from politicians and military leaders across the world.
A statement from George W Bush said: "Laura and I are deeply saddened by the death of Colin Powell.
"He was a great public servant, starting with his time as a soldier during Vietnam.
"Many Presidents relied on General Powell’s counsel and experience. He was National Security Adviser under President Reagan, Chairman of the Joint Chiefs of Staff under my father and President Clinton, and Secretary of State during my Administration.
“He was such a favourite of Presidents that he earned the Presidential Medal of Freedom — twice. He was highly respected at home and abroad. And most important, Colin was a family man and a friend.
"Laura and I send Alma and their children our sincere condolences as they remember the life of a great man."