Yes, but with some restrictions depending where you come from.
Basically all foreigners can buy property provided it doesn’t come with land.
Since 1st January 2012 EU and EEA citizens are allowed to buy land in Bulgaria, following the expiry of the 5 year prohibition included in the Treaty of Accession of Bulgaria to the EU. This means that EU and EEA citizens can buy properties that comes with land, for instance, houses, apartments sold with gardens, plots of land within the settlement limits, commercial properties, offices etc.
Under the same treaty, since 1st January 2014 EU and EEA citizens can also buy agricultural land and forests in Bulgaria without restrictions.
All other foreigners are still under the prohibition of buying land in Bulgaria but are allowed to buy any property that comes without land, for instance apartments sold without ideal parts.
Non-EU or EEA citizens have the possibility to buy property without restrictions in Bulgaria provided they register a Bulgarian company.
You can obtain additional information at:
https://www.gov.uk/how-to-buy-property-in-bulgaria
http://www.property-in-bulgaria.bg/