"Burma hasn't seen another elephant for over five years now, and we thought they would take it all pretty slowly and she would take her time to get used to a new companion.
"But this has been very quick and there's signs of a lot of lovely nice protective behaviour and early signs of intimacy. So that's very nice to see."
Keepers had been slowly introducing Anjalee and Burma in the barn - first with visual contact, then physical contact.
Anjalee arrived at Auckland Zoo on Sunday after travelling from Sri Lanka to New Zealand, via Niue for a 3-month quarantine period.
The 1.7 tonne 8-year-old elephant is here to keep 32-year-old Burma company, and Mr Wilcken said early signs of this was "so exciting".
"Anjalee is exploring her new environment, just as much as Burma is exploring her new relationship and new companionship...this is as good as we could possibly have hoped for, it's fabulous, they're very happy."
He said this was the most important social bond for Asian elephants.
"The core of Asian elephants' social unit is the female herd, the matriarchal herd."
Mr Wilcken said the two elephants would probably be spending a lot of time together from now on - welcome company for Burma who has been lonely since her friend Kashin died in 2009.