Both came to the collection as part of the European Breeding Programme (EEP) and keepers hoped that they would one day produce a litter of their own.
The two formed an instant bond and two years later, after a gestation period of four months, Kanha gave birth to three cubs – Kali, Sita and Sonika.
Lionesses rear their babies in seclusion and often reject them if they are disturbed so keepers watched the births remotely on CCTV monitors.
For nearly two months, the triplets lived solely with their mother in the birthing pen. Rana remained in the neighbouring enclosure but was never too far from the cubs, often seen by keepers taking a great interest in his new family.
This week, the cubs were successfully introduced to their father in the main lion outdoor enclosure. Kanha and Rana are proving to be exceptional first-time parents and all three boisterous newborns, sexed as female, are healthy and developing into confident young cubs.
Curator of Cotswold Wildlife Park, Jamie Craig, commented: "We have not bred Lions for many years at Cotswold Wildlife Park so it is an exciting time for the mammal keepers.
"Our young pair are proving to be exemplary parents and although there was some trepidation when we reintroduced the lioness and her cubs to the male, all went without a hitch and they can now be seen playing happily families in their enclosure."
Asiatic Lions are one of the world's rarest big cat species. Wild population numbers have declined drastically over the last century, almost to the point of extinction.
Once found throughout much of South-West Asia, they are now only found in one isolated area - India's Gir Forest. This region is the sole home to this subspecies and is considered to be one of the most important conservation areas in Asia.
This forest has shrunk to less than half its size since 2000 and Asiatic Lions are considered to be vulnerable to extinction from unpredictable events, such as an epidemic or large forest fire.
They are classified as endangered by the International Union for Conservation of Nature (IUCN).
Cotswold Wildlife Park and Gardens is open from 10am to 6pm until October. E-tickets cost £14 for adults or £15 on the gate. For children aged three to 16 E-tickets for £9.50 or £10 on the gate. Under-threes go free.