His family said he had been suffering from lymphoma.
Mr Thompson had various film roles and starred in the TV series Law & Order.
As a lawyer, he served as chief Republican counsel to the Senate Watergate Committee that investigated President Richard Nixon.
The former senator - his last term ended in 2003 - was known for his straight-talking style and booming voice.
"Fred was the same man on the floor of the Senate, the movie studio, or the town square of ... his home," his family said in a statement.
He ran for the Republican presidential nomination in the 2008 election but dropped out after failing to gain enough support.
The son of a used car salesman first achieved fame as a young lawyer for a Senate committee during the Watergate hearings in the 1970s.
His questioning of former Nixon aide Alexander Butterfield uncovered the president's secret tape recording system.
He asked the vital question: "Mr Butterfield, are you aware of the installation of any listening devices in the Oval Office of the president?"
The lawyer's acting career began when he was asked to read for a film part based on one of his high-profile cases.
He ended up playing himself in the 1985 film Marie, starring Sissy Spacek and Morgan Freeman.
Directors frequently turned to him to portray government power and he had roles as White House chief of staff, CIA director, FBI agent, rear admiral and senator.
Marie (1985): Himself
No Way Out (1987): CIA Director Marshall
The Hunt For Red October: Rear Admiral Joshua Painter
Days of Thunder (1990): Big John
Die Hard 2 (1990): Trudeau
Cape Fear (1991): Tom Broadbent
He was also cast as a fictional president in the little-known film Last Best Chance and as President Ulysses S Grant in Bury My Heart at Wounded Knee.
Years later, he became best known for his role as a district attorney in the New York crime series Law & Order.
"Fred believed that the greatness of our nation was defined by the hard work, faith and honesty of its people," the statement issued by his family said.
"He had an enduring belief in the exceptionalism of our country, and that America could provide the opportunity for any boy or girl, in any corner of our country, to succeed in life."
Mr Thompson is survived by five children, three of them from his first marriage Sarah Elizabeth Lindsey and two from his second to Jeri Kehn Thompson.
Fred Thompson: Ex-US senator and film actor dies
Former US senator Fred Thompson - who mounted an unsuccessful bid for the presidency as well as acting in films and TV - has died at the age of 73.
Latest from Euronews24
Stay Connected with
- Post-Brexit talks: We'll find out what's going on, TUC boss warns PM 0 Comment Details
- Coronavirus: Shares face worst week since global financial crisis 0 Comment Details
- Post-Brexit talks: UK prepared to walk away in June if no progress 0 Comment Details
- Climate campaigners win Heathrow expansion case 0 Comment Details
- Coronavirus: Global shares fall for fifth day in a row 0 Comment Details
- Budget 2020: Chancellor must raise taxes in first Budget, says IFS 0 Comment Details