The giraffes were born on May 10 at the Natural Bridge Wildlife Ranch, but the announcement was delayed because twins don't often survive.
Wasswa and Nakato are the only twin giraffes in the U.S. A previous set was born in 1988 but have since died.
Wasswa was born first at 95 pounds and about 4 feet tall. Nakato weighed in at 125 pounds and just over 5 feet tall.
In the East African language of Luganda, their names mean "first and second born twins." Wasswa and Nakato are reticulated giraffes, one of the most common species.
The ranch is a 400-acre animal preserve billing itself as an African safari, Texas-style. At nearly 3-months-old, a ranch spokeswoman says the twins are thriving.
The Associated Press contributed to this report.