There are 2
/gamerules that govern Command Block Output to the chat. The one you are looking for is
/gamerule logAdminCommands false
The the wiki entry on command blocks for more information.
The output message describes the success or failure of the executed command, and may be written to multiple destinations:
Chat: The output message is written to the chat text in singleplayer mode, or broadcast to all other ops in multiplayer mode, unless it has been suppressed with
/gamerule commandBlockOutput false.
Some commands may write additional text to the chat as their normal function which won't be suppressed (for example, the
/say command will write a message to the chat of all players), separate from the output message. [...]
Logs: The output message is written to multiplayer server logs unless it has been suppressed with
/gamerule logAdminCommands false.