Perry agreed to purchase the hilltop property for $14.5m (£10.8m) in 2015.
But two of the nuns who used to live there objected, and instead sold it to restaurateur Dana Hollister without the approval of the archdiocese.
Last month, a jury found Hollister intentionally interfered with Perry's planned purchase.
The businesswoman made her purchase of the eight-acre property with the co-operation of Sisters Rita Callanan and Catherine Rose Holzman, who maintained they had the authority to sell.
In contrast to Perry's multi-million-dollar purchase, Hollister paid just $44,000 (£32,000), with an agreement to pay a further $9.9 million (£7.4 million) after three years.
The sisters said they were uncomfortable about handing over the former convent to Perry who, despite coming from a church background, is known for provocative songs like I Kissed a Girl and California Gurls.
They refused to change their minds even after Perry visited to plea her case - showing the nuns "a Jesus tattoo on her wrist" and performing a rendition of the gospel hymn Oh, Happy Day.
"I found her videos," Sister Rita Callanan told the Los Angeles Times. "I wasn't happy with any of it."
However, the church and Perry's lawyers contended that the sisters did not have the right to sell the property, which they vacated in 2011.
They did not obtain the required legal blessings of Archbishop Jose Gomez and the Vatican - which must approve the sale of any property for more than $7.5 million (£5.6 million) - they argued in court.
A Superior Court judge ruled in the church's favour earlier this year, and a jury decided in November that Hollister should have been aware her purchase was invalid.
Media captionJames Cook reports: "Katy Perry thought she had bought the property for $15m"
The businesswoman acted with malice in persisting with her claim to the property, which she planned to turn into a boutique hotel, the court found.
She was ordered to pay the archdiocese $3.47 million (£2.59 million) and Perry's company, Bird Nest LLC, $1.57 million (£1.17 million) in legal fees.
On Monday, Hollister was also ordered to pay $10 million (£7.47 million) in punitive damages. Two-thirds of the sum will go to the Roman Catholic Archbishop of Los Angeles and one-third will go to Perry.
Hollister's lawyer, Michael Geibelson, said his client's assets were worth about $4 million, meaning she will not be able to pay either fee in full.
Perry now hopes to be able to complete her purchase of the convent, which includes an agreement to "provide an alternative property for a house of prayer" worth $4.5 million (£3.4 million), according to the archdiocese.
"Katy is extremely pleased with the jury's insight and understanding," Perry's lawyer told Billboard in a statement.
Hollister's lawyer has indicated she intends to appeal the ruling.
Photo copyright: GETTY IMAGES. Caption: Perry is in the middle of her Witness world tour, which hits the UK next year