I heard I can get VAT back on my new-build apartment in Austria. Is it true?

Brand new property usually attracts 20% VAT. However, if your property has a "Tourist Residence" status, then you can save all or a large part of this amount, depending on the annual length of your private use (i.e. you can claim tax rebate for all the periods when your apartment is offered for rent to visitors). 

How is VAT payable? Typically, you will pay full VAT on purchase and then reclaim it back within 2-6 months following purchase. In some cases, developers have pre-arranged an easier solution for buyers, so sometimes buyers are only required to pay a small portion of VAT (e.g. 1-2%) or other times they do not pay VAT at all. Domus Global will put you in touch with a local tax advisor to assist you with the process.