How to generate uniform random points in (arbitrary) N-dimension ball?

I've looked around and all solutions for generating uniform random points in the unit ball are designed for 2 or 3 dimensions.

What is a (tractable) way to generate uniform random points in a ball in arbitrary dimension?

To preface, generating random points in the cube and throwing out the points with norm greater than 1 is not feasible in high dimension. The ratio of the volume of a unit ball to the volume of a unit cube in high dimension goes to 0. Even in 10 dimensions only about 0.25% of random points in the unit cube are also inside the unit ball.