Yes. Apache Friends publish XAMPP for Linux on the same download page as the Windows version, and they list Debian, Ubuntu, Fedora, Red Hat, Arch and others as supported.
XAMPP by Apache Friends · Coding · Has a Linux version
XAMPP for Linux is an official download, offered in several PHP versions the same way the Windows one is.
It contains the same pieces: Apache, MariaDB, PHP, Perl, phpMyAdmin and OpenSSL.
The download is an installer file you make runnable and then start. It puts everything in one folder and
gives you a small control panel window for starting and stopping the web server and the database, so it is
close to the experience you had on Windows.
Your sites and databases come across. Copy the folder holding your site files, export your databases from
phpMyAdmin on Windows and import them on Linux, and your local projects run as before.
Worth knowing: XAMPP is built for local development on your own machine, not for running a site the public
can reach. That was true on Windows too. Many Linux users eventually drop XAMPP and install Apache, MariaDB
and PHP from their system's own app store instead, which keeps them updated automatically.
Runs each project's web server and database in its own container instead of one shared installation. Tidier for several projects, and more to learn first.
Your files: Your site files and database exports work the same way, but you set up each project rather than using one control panel.