The former prison officer, 36, beat fellow finalist Nicholas McDonald after receiving more than one million public votes.
"I don't know what to say," said the overwhelmed star, watched by thousands inside Wembley Arena, and millions more at home. "I just want to say that I love that boy to pieces, Nicky McDonald."
"He's got the most amazing voice, I love him to death."
Adding that she was "just so grateful," Sam said, "Thank you so much everybody. I really am appreciative."
Runner-up Nicholas was gracious in his defeat. "If I was getting beaten by anybody it would be Sam," he said. "I just want to say thank you to absolutely every single person who voted for me. I love you all."
As the show's winner, Sam has received a recording contract and will also support Beyoncé on the UK leg of her Mrs Carter tour in February. Her winner's single, Skyscraper, is now available and will vie for the Christmas number one spot.
A host of stars took to Twitter following the result's announcement to congratulate the singer.
Former winner Leona Lewis was among the first. "My girl @SamBaileyREAL did it!" she wrote. "Congratulations on winning @TheXFactor lady, your talent is immense x."
Sam's mentor Sharon Osbourne, who was emotional throughout much of the final, wrote, "Thank you everyone was has backed @SamBaileyREAL on @The XFactor! She couldn't have done it without all of you behind her!
"I am so blessed to have been a tiny part of @SamBaileyREAL's victory tonight on @TheXFactor," she added. "Thank you."
Former X Factor contestant Olly Murs also praised the new champion. "Congratulations MISS @SamBaileyREAL you deserve that!!", while Saturdays star Mollie King tweeted, "Soooo happy about @TheXFactor result!!! I know I'm a bit late (no shock there!) haha, but I'm SO pleased it was Sam!! SOOO deserved!!!"
It was also a special night for Gary Barlow, who confirmed it was his last night on The X Factor. The Take That star sang a duet alongside his "lifelong hero" Elton John, as the two men performed Face To Face at adjoining grand pianos.
"Not only am I finishing the show tonight, but I'm going to sing with my lifelong hero," Gary told host Dermot O'Leary. "I'm going to miss you all terribly. I love this show."
Sir Elton added, "It was so much fun watching the show, the two finalists are incredible, humble people. And what incredible singers they are.
"… The real reason I did it (the show) is because Gary has been a real friend of mine for the past 20 years, and when he picks up the phone, you do it."