Hey there OP
I moved across the country with my significant other. She moved with me after we had a solid amount of time together and we determined we wanted to stay together.
Our relationship has been excellent. I will say, however, that you realize the sacrifice that you are asking your partner to make. They are moving away from whatever network they had there, to just live with you as their only support. It is tough to transition, especially for the time it takes to get jobs and get settled into a new location. So while you may meet classmates and make friends, your significant other may be having a hard time meeting people, looking for a job, etc.
Yeah, it is working out with me and my GF, but it does take work. I asked her to sacrifice a lot. So make sure that you are serious about the relationship to ask your significant other to move. If you see in your heart that you are just having a good time, make sure you make it clear. It'd be wrong to posture before this critical, 4 year adventure, that you care for them more than you actually do.
On the other side of the coin, I had a friend that moved with his SO and she was excited to move and whatever. It turned out, maybe 8-10 months later, that she started to see someone from work. So even if you are asking selfishly for someone to move with you, they may have their own reasons for wanting to move. Thus is life. Hope all goes well for you.
Tl;DR - yes, it can work. Some people won't make it.
EDIT: Also, make sure to manage expectations well before you go. You will probably move again after graduating (residency), and half of physicians move again after that. If you are thinking long term for this relationship, it is good to let them know early what type of life and work schedule you'll have during the different periods of your schooling and future career.