If I get a new Xbox 360?

Will I be able to download my file from my other Xbox as well as have all my saved games on it? I want to buy a new 360 and download my profile on it but I'm afriad that if I do I won't be able to have my saved games on it such as minecraft and black ops 2 etc etc... I worked hard on all my games and I'm afraid I have to start all over when I download my profile on a new Xbox is this true?