The star, who featured in three 007 films and appeared alongside Timothy Dalton and Pierce Brosnan in the blockbusters, died on May 7.
Baker first appeared in Bond in the 1987 movie The Living Daylights as he portrayed the crazed arms dealer antagonist Brad Whitaker.
He returned to the iconic spy series in 1995's GoldenEye as a good guy, playing the CIA agent Jack Wade before reprising the role in Tomorrow Never Dies in 1997.
A statement from the actor's family read: "His intellectual curiosity made him a voracious reader, inspiring a great love of nature and animals, particularly cats.
"Throughout his life, Joe Don touched many lives with his warmth and compassion, leaving an indelible mark on everyone fortunate enough to know him," the statement read.
"As we say goodbye to Joe Don, we hold onto the memories and the love he shared with us.
"Though he may no longer be with us in body, his spirit will always remain, a guiding light in the lives he touched.
"Rest in peace, Joe Don. You will be dearly missed but never forgotten."
Before coming to prominence in the Bond films, Baker enjoyed his breakthrough role as Sheriff Buford Presser in the acclaimed 1973 vigilante action movie Walking Tall and felt that the movie – which told the story of a real-life lawman who stopped crime in his Tennessee town - captured the US public's imagination at the time.
He said during the 1990s: "In those days in the early '70s, I think a lot of people wanted to take a stick to (Richard) Nixon and all those Watergate guys.
"(The film) touched a vigilante nerve in everybody who would like to do in the bad guys but don't have the power and would get in trouble if (they) did. But Buford was able to pull it off."
He also featured in the 1985 BBC program Edge of Darkness, earning a BAFTA nomination.
Other credits during nearly 50 years on screen include Chevy Chase's comedy Fletch, Martin Scorsese's Cape Fear and Tim Burton's sci-fi movie Mars Attacks.
Baker never had any children but was married to Maria Dolores Rivero-Torres from 1969 to 1980.
He is survived by relatives in his home city of Groesbeck in Texas.
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