The studio audience responded with thunderous applause.
Thompson rejected the notion that he has waited too long to get into the race for the White House.
"People treat politicians sort of like the dentist -- they don't have anything to do with them till they have to," he said.
"I wasn't in the room when they made the rules, so I had to kind of follow my own lead," Thompson said, adding that he doubts voters will say: "That guy would make a very good president, but he didn't get in soon enough."
Leno joked with Thompson about how long he has been "testing the waters," asking: "Are you starting to get a little wrinkly?"
"These wrinkles don't come from the water," Thompson, 65, replied, to laughter. Referring to a guest announcement Leno made just before the segment, he joked: "I've been mistaken for Dr. Phil."
The "Law & Order" actor and former U.S. senator from Tennessee plans to begin an announcement tour in Iowa on Thursday.
Aides said Thompson will travel in a bus emblazoned with the slogan, "United in Our Core Beliefs," along with the key themes of "security," "unity" and "prosperity."
A key adviser said the two biggest issues motivating Thompson are "Islamic radicalism and the threat of terrorism reaching our shores," and a sense that "politics has broken down in the domestic arena, too."
Thompson plans to announce some politically dicey policies, including a plan to overhaul a system of entitlements -- Social Security, Medicare and Medicaid -- that some experts argue is not financially sustainable.
The former senator joins a field where the candidates, led by Mitt Romney and Rudy Giuliani, have been scrapping for months. In a decision that drew complaints from some activists, he skipped Wednesday night's debate at the University of New Hampshire for the Leno appearance.
Thompson's campaign is running an ad during the debate, being carried by Fox News Channel.
In the spot, the candidate says: "We can't allow ourselves to become a weaker, less prosperous and more divided nation. Today, as before, the fate of millions across the world depends on the unity and resolve of the American people."
The commercial was taped this weekend in the office of Thompson's home in McLean, Va.
Thompson seemed excited about finally launching a race that he said began "around the kitchen table in late March," telling Leno: "It starts right here."
The folksy Southerner is supplementing his Leno appearance, and previewing his Iowa kickoff, with a 15-minute announcement video on his Web site, www.Fred08.com.
Thompson has not raised money at the clip that some of his early advisers had suggested he would, but he has come in first or second place in several state polls.
His campaign, based in Nashville and Northern Virginia, has undergone several shakeups that have produced bad publicity, but his backers contend everything until now has been pre-season.
"I think the ship is righting itself," one adviser said in an e-mail.
"If the public responds and he has a good fund-raising month, he's in business. The staff turmoil is clearly out of the ordinary and disturbing, but the campaign now has the team it wants, and they'll be able to work together. We will know soon enough how well the stuff in front of the curtain plays."
After the Iowa events, he'll head on to New Hampshire, then down to South Carolina next week and on to Florida. He's also debuting a 30-second ad with a title that says it all: "I'm In."