CNN reported that Bumpers died at his home in Little Rock after suffering from Alzheimer's disease and a broken hip.
Bumpers, a Democrat, was the governor of Arkansas from 1971 to 1975. He served in the U.S. Senate from 1975 until retiring in January 1999.
Bumpers was best known for defending President Bill Clinton during his impeachment trial. Bumpers called the Lewinksky affair "a sex scandal," saying it was not an impeachable offense.
"For more than 40 years, Hillary and I cherished his friendship," Clinton said in a statement Saturday. "I am grateful that his advice made me a better governor and President ... I loved him. I loved learning from him and laughing with him. I will miss him very much."
Bumpers, who was known as fiscally conservative but socially liberal, faced seven candidates in his first primary and had little name recognition.
"I started out with 1 percent name recognition when I ran for governor," he said. "And I want people to understand, you can't win if you don't accept the challenge."
Bumpers went on to beat former Gov. Orval Faubus in a runoff, then Republican incumbent Winthrop Rockefeller. He won re-election in 1972.
In two terms as governor, Bumpers pushed to reorganize state government, raise income taxes for teachers' salaries and expand the state park system, according to KATV.
In 1974, he challenged Sen. J. William Fulbright for his seat in the U.S. Senate. Fulbright represented Arkansas in the Senate for 30 years before Bumpers defeated him in the primary.
The New York Times gave Bumpers the nickname "The Giant Killer" for his unexpected political victories.
In a statement on his website, Gov. Mike Huckabee (R-Ak.) said he was "deeply saddened" by the news of Bumpers' death.
"I first knew him as a political opponent and I must confess he beat me like a drum," Huckabee said.
Huckabee added that Bumpers was a "dedicated public servant" who was "extremely helpful to the state."
--Updated at 3:45 p.m.