Obama's rival, Hillary Clinton, congratulated him and told supporters in New York City that she would work for party unity.
But she did not concede the race and said she would consult with party leaders and supporters to determine her next move.
"This has been a long campaign and I will make no decisions tonight," she said.
"In the coming days I'll be consulting with supporters and party leaders to determine how to move forward with the best interests of our party and my country guiding my way."
On Wednesday George Bush, the US president, congratulated Obama on his victory, Dana Perino, the White House spokeswoman, said.
"He knows from personal experience that the presidential nominating process is a grueling one and Senator Obama came a long way in becoming his party's nominee," she said.
Meanwhile, both Clinton and Obama are due to speak at the influential American Israel Public Affairs Committee (Aipac) in Washington DC on Wednesday.
Clinton reportedly indicated in a private conference call with New York politicians earlier on Tuesday that she would be open to running as vice-president with Obama and would do all she could to help the Democrats win the White House.
The battle between Obama and Clinton was one of the closest and longest nomination fights in recent US history.
Five months of voting concluded on Tuesday night with primaries in Montana, won by Obama, and South Dakota, won by Clinton, according to NBC projections.
Obama's campaign had urged the last 150 or so undecided superdelegates to make their endorsements before the voting ended and a steady flow complied, making their announcements throughout the day to give Obama the 2,118 votes he needed to defeat Clinton.
Praise for Clinton
Praising Clinton in his speech on Tuesday, Obama said he was a "better candidate for having had the honour to compete with" her, and that she would be "central" to a Democratic presidential victory.
|Clinton congratulated Obama but |
refused to concede [AFP]
Obama is expected to be crowned the Democratic nominee at the party's convention in August to face Republican John McCain in November's election, and the first term senator was already training his sights on his next opponent.
"Tonight, we mark the end of one historic journey with the beginning of another," Obama told a cheering victory celebration in St Paul, Minnesota, at the site of the Republican convention in September.
He said he respected McCain's "many accomplishments even if he refuses to acknowledge mine".
But "this is our time to offer a new direction for this country that we love," he said.
McCain held a rally in Louisiana to kick off the race against Obama on Tuesday, seeking to distance himself from George Bush, the current president.
He also questioned Obama's judgment and willingness to put aside partisan interests.
|McCain kicked off his general election |
campaign by attacking Obama [AFP]
"He is an impressive man, who makes a great first impression," McCain said of Obama.
"But he hasn't been willing to make the tough calls, to challenge his party, to risk criticism from his supporters to bring real change to Washington. I have."
Obama questioned the extent of McCain's independence and tied him to Bush.
"While John McCain can legitimately tout moments of independence from his party in the past, such independence has not been the hallmark of his presidential campaign," he said on Tuesday.
"There are many words to describe John McCain's attempt to pass off his embrace of George Bush's policies as bipartisan and new. But 'change' is not one of them."