Richard Huckle, 30, from Ashford in Kent, admitted the offences against victims aged between six months and 12 years, from 2006 to 2014.
It is believed Huckle abused up to 200 children.
His sentencing hearing began at the Old Bailey on Wednesday, and is expected to conclude on Friday.
The 91 charges related to 23 children from mainly poor Christian communities in the Malaysian capital of Kuala Lumpur.
He admitted 71 of the charges, and the prosecutor asked that the other counts "lie on the file".
Huckle, a freelance photographer, was arrested at Gatwick Airport by National Crime Agency officials in December 2014.
Details of the abuse can only now be reported because investigators had previously sought a court order to ensure the victims were safe from other online sexual predators.
Huckle, a practising Christian, first visited Malaysia on a teaching gap year when he was 18 or 19. He then went on to groom children while doing voluntary work.
Investigators uncovered numerous indecent pictures and videos Huckle took of himself abusing girls and boys. More than 20,000 indecent images were found on his computer.
Huckle wrote a paedophile manual called "Paedophiles And Poverty: Child Lover Guide", as well as a series of notes in which he detailed rapes and various sex acts.
The encrypted manual was on Huckle's laptop ready for publication on the "dark web". At his first plea hearing at the Old Bailey, it took more than an hour to read out all the charges.
According to one charge, Huckle had said: "I'd hit the jackpot, a 3yo girl as loyal to me as my dog and nobody seemed to care."
At an earlier hearing, Judge Peter Rook QC told Huckle the charges amounted to "sexual offending of the utmost gravity" and said he was "considering life sentences in your case".
By Angus Crawford, BBC News
One word and a freckle indirectly led to Richard Huckle's arrest.
Police in Australia and Europe were aware of a paedophile site called the Love Zone hidden in the so-called dark web. It was protected by passwords, encryption and specialist software. Users were totally anonymous.
The images and videos there were particularly disturbing - showing the abuse of babies and very young children.
Members had to post increasingly graphic material to remain on the site. There were tens of thousands of accounts.
Officers with Task Force Argos in Australia knew the creator of the site used an unusual greeting - the word "hiyas".
After exhaustively trawling chatrooms and forums in the open internet, they found a Facebook page of a man who used the same greeting.
Although the Facebook page was fake, they identified a picture of a vehicle and that led them to a man called Shannon McCoole - a child care worker in Adelaide.
When officers went through his door, he was actually online running the site.
They took detailed photographs of McCoole's hands. This is where the freckle comes in - one on his finger matched exactly one seen in many of the images of abuse.
In an unprecedented move, Task Force Argos assumed McCoole's identity and took over the running of the site.
Last year he was given a 35-year prison sentence.
One user who stood out was Huckle - given the number of children he had access to and his aggressive attitude.
Using data gleaned from the site and information Huckle had posted on social media and other open internet sites, they identified who he was and where he lived.
Realising he was coming back to the UK for the Christmas holidays in 2014, they tipped off Britain's National Crime Agency.
As he landed at Gatwick airport he was met by officers from the NCA's Child Exploitation and Online Protection command.
On his computer and encrypted drives they found tens of thousands of obscene images and videos.
A British man is facing multiple life sentences for numerous sex crimes against Malaysian children which he boasted about on the "dark web".