We use induction and interpolation techniques to prove that a composition
operator induced by a map $\phi$ is bounded on the weighted Bergman space
$\A^2_\alpha(\mathbb{H})$ of the right half-plane if and only if $\phi$ fixes
$\infty$ non-tangentially, and has a finite angular derivative $\lambda$ there.
We further prove that in this case the norm, essential norm, and spectral
radius of the operator are all equal, and given by $\lambda^{(2+\alpha)/2}$.