PHOTOS: Obama, Romney on Election Day
PHOTOS: Obama's McCormick Place Celebration
"You reaffirmed the spirit that has triumphed over war and depression, the spirit that has lifted this country from despair to the heights of hope. We are an American family and we rise and fall as one nation," Obama said.
Thousands of supporters -- volunteers and staff -- cheered and chanted, "Four more years! Four more years!"
Obama was joined at McCormick Place by his wife, first lady Michelle Obama, and their daughters, Sasha and Malia. The first family walked out on stage to Stevie Wonder's "Signed, Sealed, Delivered I'm Yours."
He thanked his family and joked with his daughters.
"One dog's probably enough," Obama said to his daughters. In 2008, they got their dog, Bo, after moving into the White House.
He also thanked his supporters and volunteers.
"I want to thank everyone who voted in this election, whether you voted for the very first time or waited in a line for a very long time," Obama said. "Whether you pounded the pavement or picked up the phone, whether you held an Obama sign or a Romney sign, you made your voice heard. And you made a difference."
Republican Mitt Romney called Obama to concede the race and then addressed a crowd of supporters who gathered in Boston on Election Night 2012.
"This is a time of great challenges for America, and I pray the president will be successful in guiding our nation," Romney said.
President Obama said Wednesday morning he wants to meet with Romney to discuss how they can work together.
"That is where we must begin. A decade of war is ending. A long campaign is over," Obama said. "Whether I earned your vote or not, I have heard you... And I return to the White House more inspired than ever about the future that lies ahead."
Late Tuesday evening, ABC News projected President Obama and Vice President Joe Biden had the 270 electoral votes needed to secure a second term in the White House.
Shortly after the projections were announced, Pres. Obama tweeted, "Four more years,'' with a picture of him hugging first lady Michelle Obama.
He followed up with another tweet, "We're all in this together. That's how we campaigned, and that's who we are. Thank you."
The president also sent an email to supporters: "I'm about to go speak to the crowd here in Chicago, but I wanted to thank you first.
I want you to know that this wasn't fate, and it wasn't an accident. You made this happen.
You organized yourselves block by block. You took ownership of this campaign five and ten dollars at a time. And when it wasn't easy, you pressed forward.
I will spend the rest of my presidency honoring your support, and doing what I can to finish what we started.
But I want you to take real pride, as I do, in how we got the chance in the first place.
Today is the clearest proof yet that, against the odds, ordinary Americans can overcome powerful interests.
There's a lot more work to do.
But for right now: Thank you.
Around 10:30 p.m. Tuesday, ABC projections showed Obama had 275 electoral votes compared to Republican challenger Gov. Mitt Romney's 203 electoral votes. By 12:30 a.m. Wednesday Obama had a projected 303 electoral votes and had pulled ahead in the popular vote.
But those numbers were fluid throughout the evening, and the neck-to-neck race made for a tense election night with key swing states hanging in the balance.
Even before the projections were final, thousands of Obama's supporters and staff celebrated at Chicago's McCormick Place.
Chicago Fire Department personnel actually had to treat a number of people near the front of the president's stage after they became ''overheated'' while standing and waiting for the president to speak. Fire department officials say everyone is OK, but they suffered from overheating, difficulty breathing and some anxiety in the large crowd.
Five people were transported to local hospitals. All are in stable and good condition. And 13 people were evaluated, treated and released at McCormick Place.