(CNN) -- Barack Obama told supporters that "change has come to America," as he addressed the country for the first time as the president-elect.
"The road ahead will be long. Our climb will be steep. We may not get there in one year or even one term, but America -- I have never been more hopeful than I am tonight that we will get there. I promise you -- we as a people will get there," Obama said in Chicago, Illinois.
Police estimated that 125,000 people gathered in Grant Park to hear Obama claim victory.
Obama said he was looking forward to working with Sen. John McCain and Gov. Sarah Palin "to renew this nation's promise in the months ahead." 
Watch as Obama addresses the country »
McCain on Tuesday urged all Americans to join him in congratulating Sen. Barack Obama on his projected victory in the presidential election.
"I pledge to him tonight to do all in my power to help him lead us through the many challenges we face," McCain said before his supporters in Phoenix, Arizona.
"Today, I was a candidate for the highest office in the country I love so much, and tonight, I remain her servant," he said.
McCain called Obama to congratulate him, Obama's campaign said. Watch McCain concede »
Obama thanked McCain for his graciousness and said he had waged a tough race.
President Bush also called Obama to congratulate him.
Bush told Obama he was about to begin one of the great journeys of his life, and invited him to visit the White House as soon as it could be arranged, according to White House spokeswoman Dana Perino.
With his projected win, Obama will become the nation's 44th president and its first African-American leader.
Supporters in Chicago cheering, "Yes, we can" were met with cries of "Yes, we did."
More than 1,000 people gathered outside of the White House, chanting, "Obama, Obama!"
Obama's former rival for the Democratic nomination, Sen. Hillary Clinton said in a statement that "we are celebrating an historic victory for the American people." iReport.com: Share your Election Day reaction with CNN
"This was a long and hard fought campaign but the result was well worth the wait. Together, under the leadership of President Barack Obama, Vice President Joe Biden, and a Democratic Congress, we will chart a better course to build a new economy and rebuild our leadership in the world."
The Illinois senator is projected to pick up a big win in Virginia, a state that hasn't voted for a Democratic president since 1964. Watch how this election is history in the making »
Obama also is projected to beat McCain in Ohio, a battleground state that was considered a must-win for the Republican candidate. Watch more on Obama's Ohio win »
Going into the election, national polls showed Obama with an 8-point lead.
Obama will be working with a heavily Democratic Congress. Democrats picked up Senate seats in New Hampshire, New Jersey, North Carolina and Virginia, among others. Read about the Senate races
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Senate Minority Leader Mitch McConnell held onto his seat in Kentucky.
CNN's Ed Henry said there were lots of long faces in the lobby of the McCain headquarters at the Arizona Biltmore hotel as McCain allies watched returns showing Senate Republicans losing their seats. Watch what McCain says about the race »
Voters expressed excitement and pride in their country after casting their ballots Tuesday in what has proved to be a historic election.
Poll workers reported high turnout across many parts of the country, and some voters waited hours to cast their ballots. Read about election problems
Reports of minor problems and delays in opening polls began surfacing early Tuesday, shortly after polls opened on the East Coast.
The presidential candidates both voted early in the day before heading out to the campaign trail one last time. Watch Obama family at polls »
Tuesday also marked the end of the longest presidential campaign season in U.S. history -- 21 months.
As McCain and Obama emerged from their parties' conventions, the race was essentially a toss-up, with McCain campaigning on his experience and Obama on the promise of change. But the race was altered by the financial crisis that hit Wall Street in September.
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