That's an emotional difficult task, Linkat, and everyone who's moved
long distance away from their family can relate to it. I can!
Actually, I would suggest talking to your parents alone at first. You're
their daughter, you have a more intimate relationship with them, and
they probably will feel more comfortable letting their emotions go,
while it is only you around.
I also would emphasize the extended visits and multiple visits during the year, the extra bedroom just for them, and reassure them that they're always welcome. Texas is not out of this world (although some might think so

)
If you incorporate them in the relocation preparations and the moving
itself, it might be less stressful for them. It is not going to be easy, and from experience I know that family visits and especially the good byes can be very emotional and draining.
Good luck, Linkat!