Lieberman, who could become the nation's first Jewish president, told students at his old high school that during the Bush campaign two years ago, "we were promised a better America, but that promise has not been kept."
He also reminded them that he and Al Gore won the popular vote in 2000 when he was Gore's vice presidential running mate.
"I am also proud to say, in that election, as you may remember, that Al and I got a half million more votes than our opponents, and we actually got more votes than any Democratic ticket in the history of the United States," Lieberman told students at Stamford High School.
Lieberman, 60, joins a crowded Democratic field. Former Vermont Gov. Howard Dean, Missouri Rep. Dick Gephardt, Massachusetts Sen. John Kerry and North Carolina Sen. John Edwards have already announced their candidacies. Several others are said to be considering bids.
The first Jew on a major-party presidential ticket, Lieberman was not widely known before Gore picked him to be his running mate in 2000. He dismisses the notion that his religion will make it difficult for him to be elected.
"I'm not willing to accept that," Lieberman told CBS News Correspondent Harry Smith. "America makes a promise that if you work hard and play by the rules you can go as far as your God-given talents will take you."
A centrist, Lieberman had long campaigned against violent images in the media and was a strong supporter of the Gulf War. He also drew national attention when he criticized President Clinton's affair with Monica Lewinsky from the Senate floor.
As the vice presidential candidate, Lieberman introduced many Americans to the habits of an Orthodox Jew. He refused to campaign on Saturdays, the Jewish Sabbath, although he would work or cast votes if necessary.
Lieberman said he would not favor Israel over the United States. He also earned the respect of Christian activists, embracing issues such as family, morality and reverence.
"I intend to talk straight to the American people and to show them that I am a different kind of Democrat," Lieberman said Monday. "I will not hesitate to tell my friends when I think they are wrong and to tell my opponents when I think they are right."
As Gore's running mate, Lieberman drew criticism from Republicans who accused him of softening or abandoning his positions on issues such as school vouchers and affirmative action to shore up Democratic support. Lieberman denied changing his positions.
As soon as the 2000 race was over, Lieberman was considered a prospect for 2004, and he traveled from New Hampshire to California testing support. Gore took himself out of the 2004 race weeks ago, freeing Lieberman from his self-imposed pledge not to run if the former vice president did.
A Yale Law School graduate, Lieberman was a state senator and Connecticut attorney general before winning election to the U.S. Senate in 1988.