In 1994 he and other Republicans took control of congress and established an equal counterpoint to Democrat Bill Clinton in the White House.
In the 2008 campaign, former first lady Hillary Rodham Clinton is among the Democratic candidates.
In a webcast, Thompson laid out the rationale for his candidacy: "In 1992, we were down after a Clinton victory.
"In 1994, our conservative principles led us to a comeback and majority control of the congress. Now, you don't want to have to come back from another Clinton victory. Our country needs us to win next year, and I am ready to lead that effort."
Thompson also swiped at Giuliani and Mitt Romney, without naming them. He said: "In 1994, when I first ran, I advocated the same commonsense conservative positions that I hold today."
Thirteen years ago, Giuliani was a New York mayor who espoused liberal-to-moderate positions on social issues and endorsed Democratic Governor Mario Cuomo. Romney was a moderate challenging Senator Edward Kennedy in liberal Massachusetts.
Today, some conservatives question Giuliani's and Romney's credentials - and Thompson sees an opening for his candidacy.
An actor for decades, Thompson is known as the district attorney Arthur Branch on NBC's Law & Order, and for his roles in more than a dozen films.
During his 1994-2002 senate tenure, he was considered a reliably conservative vote. However, he strayed from the party line on a few issues, including advocating for campaign finance reform.
Thompson also spent many years in Washington as a lawyer and lobbyist. He has faced repeated questions about his lobbying work for a family planning group that sought to relax an abortion rule, and for Jean Bertrand-Aristide, the former leader of Haiti.