Edwards, 62, spoke only to confirm his name, address and date of birth and indicate guilty pleas to the three charges at London's Westminster Magistrates' Court.
Asked if he wished to indicate a plea to the three charges, which relate to three different categories of indecent images, Edwards said: "Guilty."
During the 25-minute hearing, prosecutor Ian Hope said the 41 still or moving images were sent to Edwards by an adult male on WhatsApp between December 2020 and August 2021.
Mr Hope added that seven of the 41 images were of the most serious kind and that two of that seven were pornographic videos of a child possibly aged seven and nine years old.
Edwards's lawyer Philip Evans emphasised that the charges to which his client had indicated guilty pleas related only to images that were sent to him via WhatsApp.
"There is no suggestion in this case that Mr Edwards has in any way made, in the traditional sense of the word, any images in any physical way or created any images of any sort," Mr Evans said.
The offences can carry jail terms of up to 10 years.
Judge Paul Goldspring said Edwards would be sentenced on September 16.
Edwards was the BBC's highest-paid news presenter and anchored the broadcaster's BBC News at Ten bulletin for more than two decades.
He was regularly chosen to anchor the broadcaster's biggest events and announced the death of Queen Elizabeth II in 2022.
He resigned in April this year, citing medical advice, some nine months after UK media reports contained allegations he had paid a young person thousands of pounds for sexually explicit photos.
The BBC's annual salary report revealed Edwards was the corporation's third-highest paid star between April 2023 and March this year, earning around £475,000 ($933,500) in that period.
"The BBC is shocked to hear the details which have emerged in court today," the public broadcaster said in a statement.
"There can be no place for such abhorrent behaviour and our thoughts are with all those affected."
The BBC revealed that it was made aware "in confidence" in November last year that Edwards had been arrested on suspicion of serious offences and released on bail while police continued their investigation.
It added that it would have dismissed him if he had been charged, and Edwards was "no longer an employee" by the time he was charged in June this year.
Sophie Raworth, who was presenting the early evening news on Wednesday, stressed that the BBC news department is independent from the broadcaster's hierarchy.
She said it only learned that Edwards had been charged on Monday along with everyone else when the Metropolitan Police revealed he was due in court Wednesday.
/AP
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