I seem to find only partial explanations regarding this question, I've used Bluetooth in previous projects but I plan to use it on an FPGA project. Currently The FPGA is connecting using a UART module. If I were to switch the UART module with a Bluetooth module, would their be any issues or would it work without any adjustments to the HDL code?
The HC-05 indeed works with UART, though there are some points to consider.
Also mentioned by FarhadA, the HC-05 uses AT-styled (not sure if it's conform the standard?) commands. This will mean that for setting the baud-rate you'll need to send AT+UART=9600,0,1 or something equivelant.source Though, if you run it on it's default baud-rate you might just get away with it. They seem to tunnel the UART messages out of the box (when using the default baudrate)source. Though checking of a device is connected and/or settings are done through AT commands. Thus might require changes in your code.
I've seen that these devices particulary run on 5V or (3.6V to 6V)source. So it might not work directly with your (3.3V?) FPGA. You'll need something to shift the voltage, there are some 'breakout boards' for this on the market (https://www.sparkfun.com/products/12009) but I guess there are various ways to achieve this.
The RN-42 seems to be 3.3V compatible source