It's a pretty major project.

For sure you are going to need different shifters and brake levers because the ones that you have now won't fit on the slightly larger diameter dropped handlebar. The combination brake/shift levers that most of the road bikes use can get pretty pricy but, if you buy brand new ones, they'll come with the new shifter and brake cables and housings that you are going to need.

You will also probably need a new stem. Flat bar stems have a slightly smaller clamp diameter and won't fit road bars without modification. As the other poster mentioned, you might want a shorter stem to make the new confituration fit right.

I assume you have linear pull brakes. That's going to require some kind of adaptation to make them work. If it was my bike I'd use brifters and travel agents on the brakes but there are some other choices.

What are you using for a crankset and front derailleur? I haven't tried it personally so I can't say from personal experience but I'm told that road brifters and a mountain bike front derailleur doesn't work.