The Senate Appropriations Committee chairman, who was third in line for the presidency as Senate president pro tem, had been hospitalized with respiratory problems since Dec. 6.
Fox News said Inouye's wife Irene and his son Daniel Inouye Jr. were at his side when he died. Last rites were performed by Senate Chaplain Barry Black, the network said.
Inouye served in the Senate since 1963, making him the longest-serving member of the body. He also served in the U.S. House of Representatives.
According to his office, Inouye's last word was "Aloha."
The Washington Post reported his colleagues eulogized him on the Senate floor.
"His service to the Senate will be with the greats of this body," Senate Majority Leader Harry Reid of Nevada said.
Reid recalled how Inouye, who was of Japanese heritage, was asked by his son why he volunteered to fight in World War II despite the United States labeling Japanese-Americans "enemy aliens." Reid said Inouye's response was he did it "for the children. That's Senator Inouye."
Senate Minority Leader Mitch McConnell of Kentucky cited Inouye's modesty, the Post said.
"He had every reason to call attention to himself, but never did," McConnell said. "He was the kind of man, in short, that America has always been grateful to have, especially in her darkest hours: Men who lead by example and expect nothing in return."
The Post said Inouye's seat will be filled by an appointment by Democratic Hawaiian Gov. Neil Abercrombie.
Inouye's seat will be open for a full term in 2016.