Barack Obama called Mrs Clinton to congratulate her and praised her "historic campaign"
Hillary Clinton has declared victory in the Democratic party nomination race after winning at least another three primaries - but party rival Bernie Sanders refused to bow out of the contest.
In an email to fundraisers, Mrs Clinton said her campaign had broken "one of the highest, hardest glass ceilings".
She wrote: "Together we secured the Democratic nomination.
"For the first time ever, a woman will be a major party's nominee to become President of the United States."
Barack Obama phoned Mrs Clinton to congratulate her and praised her "historic campaign".
The 68-year-old becomes the first woman nominated by a major US political party to be president.
Addressing supporters at a victory rally in Brooklyn, New York, she said: "Thanks to you we have reached a milestone. The first time in our nation's history that a woman will be a major party's nominee.
"So many of you feel like you're out there on your own. Nobody has your back. Well I do... and as your president I will always have your back."
Mrs Clinton paid tribute to rival Mr Sanders, saying their debates on income inequality in the US were good for America and the Democratic Party.
And she singled out Donald Trump for criticism, claiming he was "temperamentally unfit to be president and commander-in-chief".
She won primaries in New Jersey, South Dakota and New Mexico on Tuesday night, but lost in Montana and North Dakota to Mr Sanders, who pledged to fight on as he thanked his supporters at a rally in Santa Monica, California, where votes are still being counted.
The Vermont senator said his supporters must continue to campaign to prevent Donald Trump from becoming president.
"Our mission is more than defeating Donald Trump - it is transforming our country. Democracy is not about billionaires buying elections. Thank you all. The struggle continues," he added.
According to an AP count on Monday, Mrs Clinton had already secured the 2,383 delegates she needed to clinch the nomination before Tuesday's primaries and caucuses in six US states.
She has wasted no time in turning her attentions to the general election after her campaign announced she will make stops next week in Ohio and Pennsylvania - two states that will be pivotal in November.
She now also faces the task of having to win over Mr Sanders' supporters and to unify the Democratic party behind her.
Superdelegates - senior party figures who can choose who they vote for at the convention - are free to switch that vote. The vast majority have pledged themselves to backing Mrs Clinton.
On the Republican side, presumptive presidential nominee Mr Trump won all five primaries in New Jersey, New Mexico, Montana, California and South Dakota.
Speaking at a victory rally in New York, he took aim at Mrs Clinton and her husband Bill, claiming they "had turned the politics of personal enrichment into an art form for themselves".
A Reuters/Ipsos poll on Tuesday showed Mr Trump was 10 points behind Mrs Clinton.