But the new feature will let users send and receive messages "even if your phone battery is dead".
Up to four other devices - like PCs and tablets - can be used together, WhatsApp said.
To begin with, the new feature will be rolled out as a beta test for a "small group of users", and the team plans to improve performance and add features before enabling it for everyone.
End-to-end encryption - a key selling point for WhatsApp - will still work under this new system, it said.
Several other messaging apps already have such a feature, including rival encrypted app Signal, which requires a phone for sign-up, but not to exchange messages.
But the feature has long been requested by WhatsApp users - of which there are a reported two billion.
'A rethink'
In a blog post announcing the move,Facebook engineers said the change needed a "rethink" of WhatsApp's software design.
That is because the current version "uses a smartphone app as the primary device, making the phone the source of truth for all user data and the only device capable of end-to-end encrypting messages for another user [or] initiating calls", the company said.
WhatsApp Web and other non-smartphone apps are essentially a "mirror" of what happens on the phone.
But that system has significant drawbacks familiar to many regular users, as the web app is known to frequently disconnect.
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