Clinton hails historic moment for women
"Thanks to you, we've reached a milestone," she told cheering crowds at a rally in New York.
She hailed "the first time in our nation's history that a woman will be a major party's nominee".
Earlier Mrs Clinton won the Democratic primary in New Jersey, cementing her hold on her party's nomination.
The AP news agency reported on Monday that Mrs Clinton had enough delegates to qualify as the Democratic nominee.
Six states have been voting in primaries on Tuesday but the race in California will count the most.
Her rival, Bernie Sanders, is hoping for a win in the state, where polls show the race is close.
He aims to sway super delegates to support him instead of Mrs Clinton at the party's convention in July, but commentators say the Vermont Senator is unlikely to succeed in his bid for the nomination.
"To every little girl who dreams big: Yes, you can be anything you want-even president. Tonight is for you," Mrs Clinton tweeted following her win in New Jersey.
Speaking in Brooklyn, New York, she said Republican presumptive nominee Donald Trump was "temperamentally unfit" to be president.
"My mother... taught me to never back down to a bully. Which turned out to be pretty good advice," she said.
While Mrs Clinton won in New Jersey, South Dakota and New Mexico, Mr Sanders found victory in the North Dakota caucuses.
Meanwhile Mr Trump won in his party's vote in New Jersey, South Dakota, New Mexico, California and Montana.
The billionaire turned his attention to the election in November in his remarks at Trump National Golf Club in Briarcliff Manor, New York.
"We're only getting started and it's gonna be beautiful," he said.
