Details of a fee for the transfer have not been released, but the 25-year-old is reported to have agreed a six-year contract with the Galician club.
Depor had been negotiating a deal for the South American shot-stopper for some weeks, after the player appeared in the Teresa Herrera trophy competition which was held in A Coruna at the beginning of August.
As part of the transfer, Depor players Ivan Perez and Changui will join Nacional de Montevideo on season-long loans this term with the option of permanent moves should they impress.
Munua will compete with Juanmi and Spanish international Francisco Molina for the number one jersey at The Riazor.
