When a non resident alien becomes a resident alien, what is the basis of property for depreciation purposes - does it start from the date of property purchase or does it start from date taxpayer becoming resident alien?

If it is a residential property, it does not depreciate. If it is a rental property, it depreciates from the date it was rented.

However, on your first tax return as resident of U.S. you can take the value of property based on your cost basis, improvement expenses and previous years' depreciations. With your tax return, you need to file Sch E (Form 1040) and claim depreciation each year.

Note that if the property is in a foreign country, it depreciates over 40 years vice 27.5 years for a U.S.-based property.