The audience clapped and cheered for several minutes before the former Secretary of State finally began to speak at the convention in Philadelphia.
She thanked her daughter Chelsea, who introduced her, and her husband and ex-President Bill Clinton, who gave a highly personal speech endorsing her bid on Wednesday.
Within minutes, she went on the attack against Republican nominee Donald Trump, saying Mr Trump wants Americans to "fear the future".
She told the Convention: "We have to decide if we will all work together, so we can all thrive together."
She continued: "Don't let anyone tell you our country is weak and don't believe anyone who can tell you: 'I alone can fix it'.
"Isn't he forgetting troops on the front line, teachers, entrepreneurs, mothers. Americans don't say 'I alone can fix it'. They say 'we can fix it together'."
"Stronger together is not just a lesson from history. It's a future we are going to build."
She recalled her youth and how her family had worked to make sure she had opportunities they had not, before explaining why her upbringing had inspired her attempts to improve education for disabled children.
Mrs Clinton promised to be a president for not just Democratic party supporters, but also for Republicans and independents, some of whom have lent their support to her on the podium despite being from rival parties.
Referring to her nomination as the first woman running for President from a major US party, she said: "When all the ceilings are broken through, the sky's the limit."
In a direct attack on her rival's business record, she pointed to contractors who had allegedly lost out when a Trump development was not completed and to a series of Trump products which were not made in the US but elsewhere.
"Donald Trump says he wants to make America great again. Well, he could start by actually making things in America," she added.
Highlighting occasions when Mr Trump had apparently responded to criticism, she said: "If you dare, imagine him in the Oval Office facing a real crisis - a man you can bait with a tweet, is not a man you can trust with nuclear weapons."
She was introduced by her daughter Chelsea, who spoke warmly of her mother as a woman "driven by compassion, by faith, by kindness, a fierce sense of justice, and a heart full of love."
It followed speeches and songs in support from a procession of celebrities including Katy Perry, Carole King and Chloe Grace Moretz.
Among those who spoke earlier in support was Marine General John R. Allen, a former commander in Afghanistan, who said: "We must seize this moment to elect Hillary Clinton as president of the United States of America."
But, despite making several mentions of plans she has made with her erstwhile rival Bernie Sanders, she did not have a trouble-free speech, with several in the audience heard heckling at several points before others drowned them out with chants of "Hillary, Hillary..."
Mr Trump used his Twitter feed to hit back soon after he she finished speaking, saying: "Hillary's refusal to mention Radical Islam, as she pushes a 550% increase in refugees, is more proof that she is unfit to lead the country.
"Our way of life is under threat by Radical Islam and Hillary Clinton cannot even bring herself to say the words. Hillary's vision is a borderless world where working people have no power, no jobs, no safety."