Biden made the announcement Tuesday after months of speculation over whether he'd enter the race.
"Unfortunately, I believe we're out of time, the time necessary to mount a winning campaign for the nomination," Biden said.
Clinton called Biden "a good man and a great Vice President."
"Serving alongside him in the Senate and then the [Obama] administration, I saw first-hand his passion for our country and our people. Like millions of others, I admire his devotion to family, his grace in grief, his grit and determination on behalf of the middle class, and his unyielding faith in America’s promise," she said.
"I am confident that history isn’t finished with Joe Biden," she added. "As he said today, there is more work to do. And if I know Joe, he will always be on the front-lines, always fighting for all of us.”
Sanders, an Independent senator from Vermont, called Biden a "good friend."
“I thank the vice president for a lifetime of public service and for all that he has done for our nation. I look forward to continuing to work with him to address the major crises we face," Sanders said. "He understands the need to rebuild the middle class; and to address income and wealth inequality, a corrupt campaign finance system, climate change, racial justice, immigration reform and the need for publicly-funded higher education.”