Al Bello/Getty Images
Even Republican presidential front-runner Donald Trump weighed in.
"I think Joe Biden made correct decision for him & his family. Personally, I would rather run against Hillary because her record is so bad," he wrote on Twitter.
Former Secretary of State Hillary Clinton, the Democratic front-runner whose campaign would have probably been most threatened by Biden, hailed his decision on Twitter.
"[Biden] is a good friend and a great man. Today and always, inspired by his optimism and commitment to change the world for the better," Clinton said.
"Joe Biden is a good man and a great Vice President. Serving alongside him in the Senate and the administration, I saw first-hand his passion for our country and our people," she added in a statement. "And I'm confident that history isn't finished with Joe Biden. 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."
Sen. Bernie Sanders (I-Vermont), who is running as a Democrat, similarly labeled Biden a "good friend."
"Joe Biden, a good friend, has made the decision that he feels is best for himself, his family and the country. 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 wrote.
The two other Democratic candidates - former Maryland Gov. Martin O'Malley (D) and former Rhode Island Gov. Lincoln Chafee (D) - also issued statements of support.
"Vice President Joe Biden is a very good and decent man who has served our country nobly, and his experience would have been a welcome addition to the Democratic race," O'Malley said. "I will always admire his strength in the face of adversity and his passion for bettering our country. I respect Vice President Biden's decision today and wish the Vice President and his family well."