  We find an exact analytical solution of the Y-system describing a cusped
Wilson line in the planar limit of N=4 SYM. Our explicit solution describes
anomalous dimensions of this family of observables for any value of the `t
Hooft coupling and arbitrary R-charge L of the local operator inserted on the
cusp in a near-BPS limit. Our finding generalizes the previous results of one
of the authors & Sever and passes several nontrivial tests. First, for a
particular case L=0 we reproduce the predictions of localization techniques.
Second, we show that in the classical limit our result perfectly reproduces the
existing prediction from classical string theory. In addition, we made a
comparison with all existing weak coupling results and we found that our result
interpolates smoothly between these two very different regimes of AdS/CFT. As a
byproduct we found a generalization of the essential parts of the FiNLIE
construction for the gamma-deformed case and discuss our results in the
framework of the novel ${\bf P}\mu$-formulation of the spectral problem.
