It would take Burma a bit of time to get used to the new "elephant in the room" after six years but the team was hopeful the two animals could meet within days or weeks instead of months, Mr Buley said.
"They are very capable of thinking for themselves and making their own decisions so there is an element of where, like a dating agency introducing two people for the first time, we need to do it carefully with an awareness that we've got to give them the time and space to get used to it rather than force anything.
"It's step-by-step. It's one day at a time, almost one hour at a time, seeing how they go until the point where we can actually put them together. But the early signs are encouraging," Mr Buley said.
The "common glue" for the elephants would be the elephant team at Auckland Zoo which was already developing a strong relationship with the newcomer, he said.
The team was introduced to Anjalee almost two years ago at the elephant orphanage in Sri Lanka.
It wasn't a straightforward trip for the young elephant to come to New Zealand - first she was flown in a freight plane from Colombo to Auckland in March before being transferred to a New Zealand Defence Force C-130 Hercules and flown to Niue.
Anjalee spent a lot of her three-month Niue stint chasing chickens around her enclosure.
Yesterday she spent another five hours on a plane, accompanied by an entourage of defence force personnel, before landing in Auckland and being crane-lifted into her new enclosure.
Mr Buley said the adventurous elephant would be sorely missed in Niue but was settling in well.
"It was quite moving yesterday leaving Niue, with dozens of people lining the road waving goodbye and shouting "Goodbye Anjalee". She's an incredibly stable, resilient, adventurous elephant that seems to take everything in her stride.
"She didn't get an awful amount of sleep last night but that's to be expected in a strange place...hopefully with her having a full day to settle in she'll sleep much better today."
Both elephants were very "human-orientated" and should theoretically be a good match, Mr Buley said.
Anjalee, meaning 'gracious gift', was born at Sri Lanka's Pinnawala Elephant Orphanage.
The project to bring her to New Zealand was approved in 2011 by Auckland Council, which has put $3.2 million towards it, at no cost to ratepayers.
Mr Buley said it would not have been possible without the help of the New Zealand Defence Force.
"We owe a huge debt of thanks to them for helping make this project happen," he said.
