President Maithripala Sirisena presented a deed of ownership for five-year-old "Nandi" during a red-carpet welcome in Colombo for Key, who arrived for a two-day official visit.
Nandi, born at Sri Lanka's oldest elephant sanctuary, is the second bequeathed to New Zealand in the last 12 months after baby "Anjalee" was also gifted to the Auckland Zoo.
"The first elephant has gained 700 kilos in one year," Key told Sirisena at the ceremony.
Sri Lanka has a long history of giving elephants as presents, with China gifted three over the years, and two each for Japan, South Korea, the Czech Republic and the United States.
But activists urged the government to halt the practice, saying some of the animals had found it difficult to adapt to their new climates and without their families.
"We are very disappointed," Sagarika Rajakarunanayake, head of the Sathva Mithra (Friends of Animals) group, told AFP.
Nandi has been raised in a herd of 93 elephants in a coconut grove at Pinnawala Elephant Orphanage, about 80 kilometres east of Colombo.
Local environmental lawyer Jagath Gunawardana said the government had given away too many, describing the animals as sacred in the mainly Buddhist nation.
"There should be a stop to these knee-jerk gifts of baby elephants," Gunawardana said.
The government said the elephant was given in recognition of "excellent bilateral relations".
Nandi is soon set to be flown to Auckland, where mean annual temperatures of around 15 degrees Celsius may come as a shock to a calf more used to the tropical 27 degree average in Sri Lanka.