Verdict: Partly
Partly. The Project desktop program is Windows only, but the browser version, which Microsoft is renaming Planner, runs on Linux on a paid plan and handles Gantt charts and .mpp files.
The Project Online desktop client is a Windows program. There is no Mac version and no Linux version, and running it through a compatibility layer is not something anyone should rely on for work.
Project for the web is the practical answer, and it is being folded into Microsoft Planner. It runs in a browser, so a Linux machine is no obstacle, and it covers the core of what most people use Project for: a grid of tasks, a Gantt view, dependencies and milestones. It can import and export .mpp files, which is the part that matters when a colleague sends you a plan.
What the browser version leaves out is the professional end. Baselines, critical path analysis, resource levelling, the team planner view and custom reports all stay in the Windows desktop client. If you are a project manager rather than someone keeping a task list, those absences will hurt.
There is no free Linux program that seriously replaces Project. Nothing in the usual Linux app stores does resource levelling and baselines. If your job depends on that, plan to keep a Windows machine or a Windows virtual machine rather than expecting a like-for-like swap.
Not a project tool. Calc can hold a task list with dates and a rough bar chart, which is honestly where many small plans belong anyway.
Your files: Cannot open .mpp files. Export your plan to Excel format from Project before you switch.
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