  This paper is dedicated to proving the complete integrability of the
Benjamin--Ono (BO) equation on the line when restricted to every $N$-soliton
manifold, denoted by $\mathcal{U}_N$. We construct generalized action--angle
coordinates which establish a real analytic symplectomorphism from
$\mathcal{U}_N$ onto some open convex subset of $\mathbb{R}^{2N}$ and allow to
solve the equation by quadrature for any such initial datum. As a consequence,
$\mathcal{U}_N$ is the universal covering of the manifold of $N$-gap potentials
for the BO equation on the torus as described by G\'erard--Kappeler $[19]$. The
global well-posedness of the BO equation in $\mathcal{U}_N$ is given by a
polynomial characterization and a spectral characterization of the manifold
$\mathcal{U}_N$. Besides the spectral analysis of the Lax operator of the BO
equation and the shift semigroup acting on some Hardy spaces, the construction
of such coordinates also relies on the use of a generating functional, which
encodes the entire BO hierarchy.
