<p>Building on the classical Uzawa approach and the shift-splitting technique, we develop a class of Uzawa-type shift-splitting methods and preconditioners for solving block problems of three-by-three with double saddle point matrices. Theoretical analysis confirms that the iteration methods converge under appropriate conditions, and the proposed preconditioners have computational advantages to implement within Krylov subspace acceleration. Moreover, we propose a relaxed variant for the preconditioner and analyze the spectral properties of the corresponding preconditioned matrices. Finally, numerical experiments demonstrate the practicality and efficiency of the proposed preconditioners.</p>