Partly. KeePass itself does run on Linux through a compatibility layer, and most distributions package it. Most people switch to KeePassXC instead, which opens the same database file and feels native.
KeePass by Dominik Reichl · Security & passwords · Only some of it works
KeePass 2 is written for Windows but runs on Linux through Mono, a compatibility layer, and the project
documents that officially. Debian and Ubuntu ship it as keepass2, and Fedora, openSUSE, Arch and Gentoo all
package it too, so it installs from your app store.
It works, with rough edges. The window is the Windows one drawn through a translation layer, so it looks out
of place next to the rest of your desktop. Auto-type, the feature that types your username and password into
a login box for you, needs extra setup on Wayland, which is the display system Ubuntu and Fedora now use by
default. Some setups also need extra font packages before things render properly.
KeePassXC is the reason most people do not bother. It reads and writes the same .kdbx database files, so
your existing file opens with no conversion and no export step, and it is a native Linux app that looks and
behaves like everything else on the system. Browser filling works through an extension.
Your database is just a file. Copy it across on a USB stick, open it in either app with the same master
password, and everything is there. Keep a copy of the file somewhere safe before you wipe the Windows
machine, because if you lose it and the password there is no way to recover what was inside.