System stored procedures (along with other types of system object) appear logically in the sys schema of all other databases.
To make a user-defined SP available in this way:
Create the SP in the master database's dbo schema, with a name beginning with sp_… (e.g. sp_MySystemSp).
Grant access to it for all users:
GRANT EXEC ON sp_MySystemSp TO public
Mark it as a system stored procedure:
EXEC sys.sp_MS_marksystemobject 'sp_MySystemSp'