The baby, who measures a mighty 6ft, was born late on Tuesday afternoon, to mother, 10-year-old Mia.
The father is 13-year-old Kubwa. The youngster's name means 'precious' in Swahili.
Keepers have been enjoying watching mother and son bond and they have been out into the paddock to enjoy the rare sunshine. They are expecting the young giraffe to be popular with visitors.
The zoo's assistant curator, Richard Brown, said: "Kito's arrival has delighted everyone at Dudley Zoo. "He spent yesterday in the internal den bonding with mum and we decided to let the pair of them out in the paddock yesterday to enjoy the fine weather."
He added: "He's quite a tall baby for a newborn and a very handsome chap and no doubt will fast become a favourite with visitors."
Rothschild's are the world's rarest sub-species of giraffe, originating from Uganda and west central Kenya.
They are easily identified by the colouring of their coat, which is made up of ragged brown patches separated by lighter creamier-coloured hair, with no markings to the lower leg. Each giraffe has a unique coat pattern, like a fingerprint.
Within a few hours of being born, calves can run around and are indistinguishable from a week-old calf.
They are named after naturalist, Lord Walter Rothschild.
A male giraffe can reach up to 18ft in height while a female giraffe can be as tall as 14.5ft.
They feed on the rough shoots of plants and their diet consists mainly of the thorny leaves of acacia trees.
The thorns do not bother the giraffes as they have a very rough tongue and lips.