How to change the default Notebook stylesheet

Wolfram has an article discussing precisely this:

http://support.wolfram.com/kb/29974

According to the Documentation,

DefaultStyleDefinitions is a global option that specifies the default stylesheet for all new notebooks.

The stylesheet must be located in a directory that is listed in StyleSheetPath.

Note that this option affects not only on-screen display, but also determines the default styles used by Export.

By convention the custom user stylesheets should be located in the user profile directory:

dir = FileNameJoin[{$UserBaseDirectory, "SystemFiles", "FrontEnd", "StyleSheets"}];

If the directory doesn't exists one should create it:

If[! DirectoryQ[dir], CreateDirectory[dir]];

You should put your custom stylesheet "DefaultModified.nb" in this directory and then set it as the default via

CurrentValue[$FrontEnd, DefaultStyleDefinitions] = "DefaultModified.nb";

After restarting the FrontEnd all the new Notebooks will have this stylesheet by default.

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It is worth to mention that according to Kuba's comment, StyleDefinitions are always set as a path relative to directories on StyleSheetPath, for example one can specify StyleDefinitions -> FrontEnd`FileName[{"Lectures"}, "styles.nb"] for a stylesheet "styles.nb" in a directory "Lectures" located wherever on StyleSheetPath. The same should be true for DefaultStyleDefinitions.