The catch-up app is not ready to launch alongside the revamped set top box when it goes on sale this week, but the broadcaster signalled it would be soon.
iPlayer was absent on earlier Apple TVs, despite the fact it is on other platforms including Amazon's Fire TV, Roku, Google Chromecast, Sky's Now TV box and several video game consoles.
One analyst said the move should aid sales of the new kit in the UK.
"Available on over 10,000 devices, BBC iPlayer is one of the biggest and best on-demand video services in the world, and has transformed how UK audiences watch programmes online," said the BBC's director-general Tony Hall.
"I am delighted that iPlayer will be coming to the new Apple TV in the coming months, helping to bring the BBC's distinctive and loved content to an even wider audience."
Until now, Sky was the only major British broadcaster to offer an app for the US firm's set top boxes.
The BBC has, however, allowed users to stream content from iPlayer's iPhone and iPad apps to older Apple TVs.
In September, its iPlayer team indicated it had "no plans" to change this. for the new device.
But a key part of Apple's pitch for its new box is that owners can use their voices to request programmes and movies by theme from across a range of services without having to open and close individual apps.
Users can, for example, ask for popular science fiction shows and be shown a range of suggestions from Netflix, NowTV and other apps that communicate their content with Apple's computer servers.
For iPlayer's content to be added to the list of recommendations, the service has to become a native app rather than be run off a separate device.
Earlier this month, the MacRumors news site reported that two Bournemouth-based developers had created a tvOS app they dubbed Auntie Player to demonstrate that it would be relatively easy for the BBC to support the new platform.
They noted it had taken them less than nine hours to build a working program and urged the BBC to build an official version of its own.
"iPlayer coming to the Apple TV is a landmark deal," commented Ian Maude from the research firm Enders Analysis.
"I think it's very difficult for any internet-based video streaming service to launch in the UK without it now.
"That was true for Sky's Now TV box - it was huge when it got iPlayer - and I think the same will be true for Apple."
The BBC understands that ITV has no plans to release an app for Apple TV.
Channel 4 and Channel 5's intentions are unknown.
The BBC has confirmed that its iPlayer service is coming to the new Apple TV.