I have a duplex and heat the entire house on gas on my dime. I would like to convert the upstairs unit to electric as they pay for their own utilities. Could someone please tell me if that is possible and how much it would cost?

Would I need to buy another furnace, or can they wire up directly to electric baseboards, which, I'm assuming, we would have to take out all the old iron baseboards and replace them with electric ones...

First, it will cost a lot to replace everything. An electric furnace (warm air) is not the same as a hot water boiler, whether gas or oil fired. Am I correct that you have forced hot water baseboards.
Second, the electric bill is usually higher than gas (and gas prices are going down as fracking increases in the US). So you will lose tenants after one year of paying very high rates. You are much better off just raising the rent.
One thing you can do is tell the tenant that you will gauge rent increases each year based partly on the current year's gas usage. That might encourage them to keep the heat down. Another is to install a clear plastic locked box over their programmed thermostat, set to gown down at night.