Biden, 76, made the announcement with a video Thursday morning that shows footage of the clashes in Charlottesville, Va., in 2017 that killed a counter-protester and injured 19 others at a Unite the Right rally over the removal of Confederate statues.
In the video, Biden touts himself as a civil rights advocate, in contrast to Trump, who reacted to the violence by remarking there were "fine people on both sides" in Charlottesville.
"In that moment, I knew the threat to this nation was unlike I'd ever seen in my lifetime," Biden said. "I wrote at the time that we're in a battle for the soul of this nation. If we give Donald Trump eight years in the White House he will forever and fundamentally alter the character of this nation.
"I cannot stand by and watch that happen. Everything that makes America America is at stake. That's why today I'm announcing my candidacy for president of the United States."
It's the third bid for president for the longtime Delaware senator who served as vice president under President Barack Obama. He ran in 1988 and 2008. Biden strongly considered a run in 2016 but ultimately decided against it following the death of his son Beau Biden, which took a great emotional toll on the family.
Joe Biden's political career started when he was elected in 1971 to represent Delaware in the Senate at age 29, becoming one of the youngest senators in U.S. history. He spent 37 years in the Senate, where he also served as chairman of the judiciary and foreign relations committees. His tenure in Congress is perhaps best known for his leading the charge on the Crime Act and the Violence Against Women Act in 1994. If elected president, Biden would become the oldest -- at age 77 -- to attain the office.
Biden's presidential quest comes with some controversy after several women accused him of inappropriately touching them. He posted a video acknowledging that "social norms are changing" and promised he would be "much more mindful" of people's personal space.
Biden was awarded the Medal of Freedom -- the highest civilian award in the United States -- from Obama in a surprise move during his final days in the White House in January 2017.