Kamran and Ketan were born at Bristol Zoo Gardens on November 9, but their arrival has only just been officially announced.
The zoo was forced to make the rare and difficult decision to hand-rear the cubs after their mother, Shiva, began "mis-mothering" following the death of their father.
Lynsey Bugg, assistant curator of mammals said: "The initial transition was a very important time for the cubs.
"We placed straw from their previous enclosure on the ground for familiarity, and gave each cub a cuddly toy to snuggle into to mimic mum.
"We also worked closely with the vet team to monitor their fluid intake while we got both cubs used to feeding from artificial teats."
Kamal was an "important male" for the conservation breeding programme, and a spokeswoman for the zoo said the a decision to hand-rear his cubs was made to give them the best chance of survival.
The lion cubs are an important part of the breed's future with only about 300 Asiatic Lions remaining in the Gir Forest Sanctuary in Northern India.
A team of five keepers are now dedicated to the cubs' care.
Each day Kamran and Ketan have their weight, temperature and respiratory rate checked.
"Alongside the challenge of feeding you need to be mindful of everything you do when hand-rearing," Ms Bugg said.
"We need to prevent the cubs from imprinting on the keepers, so we make sure we treat them the way that their mum would when we handle them."
This involves picking them up by the scruff of the neck and brushing them with a coarse brush - which replicates them being licked by their mother's tongue.
Now 10 weeks old, both cubs are beginning to reveal their individual personalities.
"They are very, very different," Ms Bugg said.
"The larger cub, Katan, is very boisterous, he really loves trying to wrestle, he is always wanting to instigate most of the play sessions, and actually his brother, Kamran is the braver of the two, if there is a situation that they're not quite sure about, it will be Kamran who goes to investigate it first.
"It is quite interesting to see how different they are, but they are brilliant together, they really bounce off each other."
Ms Bugg said she was proud of how her team had worked together to care for the cubs, but that she will not deem the hand-rearing a success until they are fully weaned and go on to breed themselves.
As the cubs are still very young, they are off show to zoo guests, but can be seen via a video link shown on a screen at the front of the lion enclosure.