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Mike Brookes, the lawyer for Church, told the High Court in London that the singer had endured "distress and embarrassment" because of the story.
Headlined 'Marryoke - Charlotte proposes after pub karaoke session', and published on November 6 of last year, the story alleged that Church had proposed to her boyfriend Jonathan Powell on a "boozy pub karaoke night" in Cardiff.
The piece claimed that Church "celebrated into the early hours" and later had to be "helped" into a taxi by friends.
Mirror Group Newspapers, publisher of The People, has already accepted that the story was "completely untrue and should not have been published".
The People published an apology to Church last year, which said: "On November 6, 2011, we said Charlotte Church had proposed marriage to Jonathan Powell at a boozy karaoke night at the Robin Hood pub in Cardiff. We were misinformed.
However, the singer opted to pursue legal action over the damage to her reputation that the article had caused.
Today, Mirror Group Newspapers again apologised to Church and agreed to pay her substantial legal damages along with her legal fees, as well as promising not to repeat the allegations.
The exact amount of damages to be paid to Church has not been disclosed. She was not in court to hear the verdict.
Brookes, of the solicitors firm Lee & Thompson, told reporters: "For the avoidance of doubt, Charlotte was not publicly or otherwise drunk at the event, did not require any help into her car, did not order a bottle of champagne each for herself and Jonathan, and did not propose to him.
"Charlotte brought this claim because the defamatory allegation that she had made a drunken spectacle of herself whilst making a proposal of marriage hurt her and caused her distress and embarrassment with her friends and family, not least which included Jonathan."
Speaking at the Leveson Inquiry shortly after the People article was published last November, Church discussed the negative attention and harassment she has endured since finding fame as a child star.
"I feel strangely strong because I've survived it all and I don't know how because at times it really messes with your mind," she told the inquiry into press ethics and standards.
"In a way I think it's made me stronger but professionally because I've been made a caricature for so long and that really isn't me, the person I am or the way I live my life.
"I think that has had a massive impact on my career. As an artist and a singer, I find it really hard to get taken seriously as my credibility has been blown to bits by this publicity."
