The male calf arrived at the Bewdley attraction on Tuesday afternoon – the first to be born on site in the park's 47-year history.
The rhino calf's parents, 11-year-old mother Seto and dad, 12-year-old Rap, can often be spotted by guests at the Asiatic section of the drive-through safari, near to the Indian rhino house built at the park in 2009.
Both Seto and her calf are said to be bonding well together in a private area where keepers can observe them at a safe distance as they settle in. He will eventually join his family in the Wild Asia section of the reserve.
The calf is currently unnamed, but his name will begin with the letter 'I' like all other animals born on-site in 2020.
Shelley Tudor, deputy head keeper of Ungulates, said: "We are absolutely delighted and have been waiting a long time for this moment.
"After holding this species of rhino for more than 10 years, this is our first calf to be born at the park.
"We acquired Seto and Rap as youngsters and have been able to watch them grow and mature over time – which makes it even more momentous to see them produce their own calf.
"He is a very special addition to the Asian rhino house, and we look forward to watching him develop, and maybe go on to produce his own little rhinos in the future."
Also known as the greater one horned rhinoceros, Indian rhinos are placid animals who are often recognised for their armoured and prehistoric appearance.
West Midland Safari Park is home to two types of rhinos – six southern white rhinos and three Asian rhinos. Both species face threats in the wild such as poaching and habitat loss – and are classed as 'near threatened' for the white rhino and 'vulnerable' for the Asian rhino, by the International Union for the Conservation of Nature.