Process for installing an offshore tower, specifically a substructure, which basically comprises the following steps: a) dry manufacturing a foundation comprising a block (1, 1′) basically made of concrete and dry manufacturing a base section (25) of a shaft (2); b) applying said base section to said foundation block, forming a unit called the “starting unit”; c) moving said starting unit to the installation point of said substructure; and d) actuating in a controlled manner, first ballast valve means in such a manner that said starting unit sinks until resting on the seabed; having placed said foundation block or said starting unit in the body of water where the installation point said substructure is located.