The conditions for adsorption of a polyelectrolyte chain in a salt solution onto uniformly charged spherical and cylindrical surfaces are derived using a combination of variational procedures and the ground state dominance approximation. Explicit formulas are obtained for the dependence of adsorption characteristics on temperature, the Debye screening length, polyelectrolyte charge density, molecular weight, and curvature. The density profile of adsorbed polyelectrolytes is determined as a function of these parameters.