Yes. Signal publishes an official Signal Desktop for Linux alongside the Windows and Mac versions, and it works the same way.
Signal by Signal Foundation · Chat & video calls · Has a Linux version
Signal Desktop supports Mac, Windows and Linux. On Linux you either add Signal's own software
source so it updates with the rest of your system, or download an AppImage, which is a single file
you run without installing.
The catch is the same one Windows users already live with. Signal must be installed on your phone
first, and the desktop app is linked to it. There is no way to use Signal on a computer without a
phone account.
Nothing is lost by leaving Windows. Your account belongs to your phone number, and linking the new
computer takes a minute. Older messages from the Windows desktop do not follow you across, because
Signal keeps desktop history on the machine itself.
Setting up the software source route means typing commands in a terminal. If you would rather not,
take the AppImage and save it somewhere you will find it, or install Signal from your system's app
store if it offers it.