The settlement, one of the highest to be paid out in the phone-hacking scandal, includes 300,000 pounds in legal costs.
The singer said afterwards she had been "sickened and disgusted" at what she called the industrial scale of the paper's illegal activities.
Lawyers for the 26-year-old and her parents, James and Maria, confirmed last week that terms had been agreed with News Group Newspapers (NGN).
The court heard that 33 articles in the News of the World were the product of hacking into her family's voicemails when Church was a teenager.
Her phone had been hacked in 2002 and journalists also placed her under surveillance and gained access to her medical records.
The court was told that her mother had been coerced into an interview with the paper about how Maria had harmed herself and attempted suicide after reporters gained information from hacked voicemails about her medical history.
Reading from a statement after Monday's hearing, the Welsh singer said: "What I have discovered as the litigation has gone on has sickened and disgusted me.
"Nothing was deemed off limits by those who pursued me and my family, just to make money for a multinational news corporation."
Church, who gave evidence to the ongoing Leveson inquiry into British press conduct last November, was one of several high-profile figures who have launched legal action against the British arm of Rupert Murdoch's News Corp.
Deals in 15 cases were agreed earlier this month while a further 37 claims were settled in January, with payouts ranging from about 40,000 to 130,000 pounds. Others are in the pipeline.