What Marie-Zug has told you isn't completely wrong, however the expatriate tax status is not granted to everyone and is subject to strict conditions. You, or your company, would first have to demonstrate that you are here either on temporary assignment within your company or that you are here as a specialist on a fixed term contract for a specific project.

You specifically cannot get a tax break for the rent of your property abroad, but you can get breaks for a whole slew of other things, limited to 5 years. Expatriate status is not a given and depends very much on the canton in which you live.

You don't say where you are moving to so I have attached the guidelines for Zurich and Aargau as examples (both in German I am afraid).