"Thanks to you, we've reached a milestone, the first time in our nation's history that a woman will be a major party's nominee," Clinton, 68, told her supporters at her campaign headquarters in Brooklyn, New York.
President Barack Obama congratulated Clinton for securing the 2,383 delegates necessary to clinch the Democratic party's presidential nomination.
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"Her historic campaign inspired millions and is an extension of her lifelong fight for middle-class families and children," White House Press Secretary Josh Earnest said.
Obama called both Clinton and Sanders to applaud them for "running inspiring campaigns that energised Democrats." The President will meet Sanders at the White House on Thursday at the Vermont senator's request, Earnest said in a statement.
Clinton, who won California, New Jersey, New Mexico and South Dakota, now has 2,755 delegates or more than half of the 4,051 total pledged delegates while Sanders has 1,852.
However, Sanders, who won in Montana and North Dakota, refused to concede defeat to Clinton, vowing to stay in the Democratic nomination race.
"Next Tuesday we continue the fight," Sanders told a large crowd of cheering supporters gathered in Santa Monica.
"We are going to fight hard to win the primary in Washington DC, and then we take our fight for social, economic, racial and environmental justice to Philadelphia."
Sanders, 74, has been facing mounting pressure to drop out of the race amid calls for Democratic party unity.
In the November presidential elections, Clinton would face fellow New Yorker Donald Trump, from the Republican party, who she said is not fit to lead the country.
If elected in November, she would be the first ever woman President of the US.
"To every little girl who dreams big: Yes, you can be anything you want, even president. Tonight is for you," Clinton said.
"We cannot let a man who demeans women, attacks people for their race or religion, and traffics in paranoid conspiracy theories take the oath of office," she said, attacking 69-year-old Trump.
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