O'Bannon, who fell ill Monday while attending a conference in Chicago, died at Northwestern Memorial Hospital, press secretary Mary Dieter said.
O'Bannon died at 11:33 a.m., a statement from his press office said.
He was "one of the most marvelous people to ever grace this Earth, and everybody should have known him," Dieter told CBS News, Radio.
"The governor experienced a drop in both blood pressure and heart rate. Based on the governor's living will, First Lady Judy O'Bannon and the family decided to use no further means of support and care and the governor died naturally," the statement said.
Although he suffered a genetic condition that gave him tremors, his most recent physical had not turned up any medical concerns, Dieter said.
The last governor to die in office was Missouri's Gov. Mel Carnahan, who was killed in a plane crash in October 2000 while campaigning for the U.S. Senate.
O'Bannon's tenure began brightly with the economic boom of the late 1990s. Indiana built a record $2 billion surplus, and O'Bannon cut taxes by $1.5 billion, put 500 more police officers on the streets, and won increasing funding for schools and universities. The moderate Democrat coasted to re-election in 2000 over former U.S. Rep. David McIntosh.
Shortly into his second term, the economic good times soured into a recession. Indiana lost 120,000 jobs, and tax revenues flowing into state coffers slowed to a trickle, forcing tax increases and cuts in social services and other agencies while largely sparing education.
Lt. Gov. Joe Kernan was serving as acting governor. He was to be sworn in as Indiana's 48th governor Saturday evening by Indiana Supreme Court Justice Theodore Boehm.
Republicans blamed O'Bannon for only recently focusing on economic development.
In an April 2002 interview, O'Bannon acknowledged the state's worst fiscal crunch in two decades would help shape his legacy.
"It will certainly be a part of it. But I don't even think of my legacy. I just look at things I can get done," O'Bannon said.
His critics also accused O'Bannon of running a loose ship as governor. They pointed to the embezzlement from a public retirement fund, a slow response by his environmental agency to a big fish kill, and problems at two state centers for the developmentally disabled.
Criticism of O'Bannon rarely turned personal, though. That reflected his folksy image — his home is a reconstructed barn on the outskirts of the family hometown of Corydon — and the goodwill he had built during 18 years in the Indiana Senate and eight as lieutenant governor.
State Rep. Brian Bosma, the Indiana House minority leader, clashed with O'Bannon on policy issues, but knew the governor's positions were deeply held.
"He has always done what he has felt was in the best interest of our state. I would never question his integrity or his service or his dedication," said Bosma.
Sen. Evan Bayh, who was governor when O'Bannon was lieutenant governor, hailed him after he fell ill Monday as "a good man and one of the most decent public servants I've ever had the honor of working with."
O'Bannon won his first term as governor in 1996, narrowly defeating Indianapolis Mayor Stephen Goldsmith, who had advocated bold moves such as school choice and privatization of government services.
Indiana residents traditionally have embraced change only when it honors the past, historian James Madison has written. "When forced to change, they were always able to blend the old with the new."
"I think O'Bannon is a wonderful combination of past, present and future," Madison, a historian at Indiana University, said in 1996.
O'Bannon took positions that many of his Democratic counterparts in other states might deem too conservative. He wanted to place a 7-foot stone monument with the Ten Commandments on the grounds of the state Capitol until the courts said no.
While a legislator, he had been the prime sponsor of the legislation that reimposed Indiana's death penalty in the 1970s. As governor, O'Bannon allowed seven executions to occur without delay but recently granted a 60-day reprieve in one case to allow for DNA testing.
O'Bannon had succeeded his father in the state Senate in 1970 and held the seat until becoming lieutenant governor. He had actually sought the governor's seat in 1987, but after Bayh entered the race, O'Bannon became the much younger man's running mate. The pair won election that year and then won a second term in 1991.
As lieutenant governor, O'Bannon quietly built ties with farmers, business people and party leaders in preparation for his own gubernatorial run. He was not opposed when he sought the Democratic nomination for governor in 1996.