Rodrigue died Saturday at a hospital in Houston, The Advocate of Baton Rouge, La., reported Sunday.
The Cajun artist's "Blue Dog" paintings brought him to prominence in the 1990s and became iconic to Louisiana, the newspaper said.
His family said he was an advocate of the arts and arts education his entire life.
"While we mourn the loss of a great man, we also celebrate his rich life and legacy," a statement from his family said. "George will remain a presence in the hearts of the people who got to know him and his work will continue to inspire for generations to come."
Louisiana Gov. Bobby Jindal said Rodrigue was one of the state's favorite sons.
"His work as an artist is iconic and uniquely Louisiana," Jindal said in a statement. "George's 'Blue Dog' not only became symbolic of his work, but it became a symbol for Louisiana. This earned him the ability to paint the likes of world leaders including Ronald Reagan, George H.W. Bush, and Bill Clinton."