Lucy, 8, arrived at Blair Drummond Safari Park.
She had been transferred from West Midland Safari Park, in Bewdley, Worcestershire, as part of a European breeding programme.
Lucy travelled more than 300 miles (483km) to her new home last night.
Blair Drummond will be sending its two-year-old female, Ailsa, to West Midland, in order to avoid any in-breeding among both parks’ rhino populations.
After sniffing the ground for several minutes, she tentatively took her first steps around the enclosure.
Chris Lucas, head of large mammals, said: “We need to exchange rhinos.
“Ailsa, who is with us... the only mature bull rhino we’ve got here is her father (Graham) so it’s not practical to keep her here.
“With Lucy as well, she was housed with her mother before coming here, and there’s lots of anecdotal evidence that daughters held with their mothers don’t go on to breed, almost as though they are suppressed.
“Also, in December last year Dot gave birth to Ailsa’s brother, Angus, and now Dot has to focus all her attention on raising him.
“Exchanges are becoming more common now. Lots of zoos and safari parks across Europe are working together with the idea of exchanging their rhinos in order to maximise the breeding potential of the captive European population.”
White rhinos are classed as “near threatened” in the wild, with a population of only 17,500, Mr Lucas said.
Lucy will be given time to adjust to her new surroundings before being introduced to the park’s other rhinos - Dot, Graham and their five-month-old calf, Angus.
It is hoped that Lucy and Graham, Blair Drummond’s only mature bull rhino, will eventually mate.