Just swap the cable and power supply over and then reboot; make sure the jumper on the rear is set to Master.
Windows will automatically find the new hardware and install the basic CDROM driver, which is all that is required.
The operation of the drive is controlled by your burning software.
Incidentally it's worth keeping your ROM drive for installing software, playing audio CDs and DVDs etc - rewriters are not the most robust of hardware and if they are used for their main purpose i.e. burning, they will last longer.
If you do, the ROM will need the jumper sett to Slave and, like the rewriter, will install automatically. Note that the rewriter will be the D drive and the ROM the E drive.
Current set up: External DVD+/-/R/RW/RAM writer. Internal DVD+/-/R/RW Lightscribe writer. Internal DVD ROM.
I am going to replace the DVD ROM with a new internal DVD+/-R/RW/RAM Lightscribe writer so I will then free myself of the external unit & associated cables whilst still keeping the multi format capability of that drive + Lightscribe of course.
Just to recap the final set up will give me two all singing & dancing internal DVD writer drives rather than just one & a ROM.
I know some think it good to keep a ROM drive but on further web investigation the general trend is to replace with a writer.