Speaking in Brooklyn, New York, he called Donald Trump the "most dangerous president" in recent US history.
Mr Sanders, a 77-year-old independent senator for Vermont, lost the 2016 Democrat race to Hillary Clinton.
He faces a much more crowded field this time but brings name recognition and a passionate support base.
More than 10 others are also running to be Democrat candidate, including Massachusetts Senator Elizabeth Warren, New Jersey Senator Cory Booker and the Mayor of San Antonio, Texas, Julian Castro.
His speech promised a presidency that would "bring people together". He outlined numerous policies and attacked greed and the "billionaire class". As president, he said he would:
- Enact a "federal jobs guarantee" to ensure all Americans have work
- More than double the minimum wage from $7.25 (£5.50) to $15
- Pass "comprehensive" immigration reform, including allowing hundreds of thousands of undocumented migrants to stay in the US
- Make universities and colleges tuition-free
- Reform healthcare to give universal coverage
He promised to fight for "economic justice, social justice, racial justice and environmental justice".
One of the challenges Mr Sanders faces is that the Democratic Party has shifted to the left, making his message less distinctive, BBC North America reporter Anthony Zurcher says.
Speaking to the BBC, Mr Sanders's brother Larry said the Vermont senator was right to try again for the presidency.
"I think Bernard's presidency would be really uplifting, finally to have somebody who people see as honest and has been committed for such a long time to be saying that we don't need the poverty, we can have all the things that we need," he said.
"It's all been a kind of crazy dogma that 'oh no, no, no, you can't afford that'."
Mr Sanders was born in Brooklyn, and the backdrop for his speech gave him an opportunity to contrast himself with the president.
He grew up as the son of a Jewish immigrant who worked as a paint seller, while Mr Trump, who also was born in New York, was the son of a wealthy real estate developer.
"I did not have a father who gave me millions of dollars to build luxury skyscrapers, casinos and country clubs," he said.
"But I had something more valuable: I had the role model of a father who had unbelievable courage in journeying across an ocean, with no money in his pocket, to start a new and better life."
As he was speaking Mr Trump was addressing a conference of conservative activists, in which he attacked the Democrats and promised he would win re-election.