Lawyers won a landmark appeal for Sandra in 2014, arguing she was being detained in Buenos Aires illegally.
The ruling found her to be Argentina's first "nonhuman person, with the right to liberty".
The 33-year-old arrived in Kansas on Friday and will undergo tests before moving to her new home in Florida.
Judge Elena Liberatori - who has a picture of Sandra in her office - told AP news agency she wanted her ruling to send a message: "That animals are sentient beings and that the first right they have is our obligation to respect them."
Sandra was born in an East German zoo and sold to Buenos Aires in 1995.