Advisor transferring to better school I am currently at a Top-20 engineering school in the US. I am making great progress on my PhD and have an excellent relationship with my advisor. 

My advisor is transferring to a Top-3 engineering school and wants to bring me.

I am concerned because I'm afraid that the Top-3 school will reject me (average undergrad GPA, crappy GRE, etc.). The good things I have are a fellowship with 3 more years of tenure, a high quality paper and a few talks. 

Anyways, when advisors move does the new university just automatically accept students? I'm afraid that my bad undergrad GPA and GRE score will keep me from following my advisor and doing the research that I love.
The other school is hiring your adviser because they think they'll be a good researcher and faculty member. This means that at some level they trust your adviser's judgement.

It's not impossible, but it'd be highly unlikely that they would refuse to admit you against your adviser's request. The more likely situation, if they're concerned about your ability, is that they would ask to have you repeat some courses or milestones like an oral exam or portfolio review.

When they hire your adviser they're essentially saying that they're impressed with their research program. It'd be a little self-defeating to hire that person but say that they can't bring substantial portions (the students) of that effort.