I'm getting a new xbox but I'm stuck with something?

I have an xbox 360 with 4gb but I need a lot more for my games so I'm getting a 250 gb one but I have bought minecraft and downloaded it from the store on xbox but is there a way I can get it off of my old xbox onto my new one
P.s I have an xbox live accout and I will continue to use it on my new one

Yes, once you have bought it on your account, you can go to the Xbox Live store, and download it for free as long as you use the same account as you have mentioned.

Go into your download history and redownload it.

Yes you can re-download it. Just go to the xbox store and find minecraft then you can download it from there for free as you have already purchased it before as long as you are using the same account you bought it on ( as you mentioned )