Unfortunately, it only works with accessories that support Fast Pair so you will not be able to use this feature with existing headphones. At the moment, only the Google Pixel Buds and the Libratone Q Adapt On-Ear headphones support Fast Pair.
Ease of use, speed and security are the design principles driving the Fast Pair specification. Fast Pair uses BLE (Bluetooth Low Energy) for advertising and discovery and uses classic Bluetooth for pairing. Here's what a Fast Pair flow looks like:
Turn on a Fast Pair-enabled device and put it in pairing mode. Android scans for BLE broadcasts in close proximity of the user's phone and discovers a Fast Pair packet (provided Bluetooth and Location is turned on).
This packet is sent to our servers to get back the device's product image, product name and companion app (if there is one).
The user receives a high priority notification asking them to "Tap to pair" to the device. The notification contains the product name and image. When the user taps on the notification, we use classic Bluetooth to establish a connection.
A success notification is shown which contains a link to download the companion app (if there is one).
More at the Android blog.