I think it is a good question. When there is yesterday morning and tomorrow morning, why have an exception for this morning (which means today's morning)? Yes, idiom, but I actually do like idiomatic extensions like these - as long as everybody knows what is meant and no grammar or semantic rules are violated...
The 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language, would consider words like yesterday, today, tonight, and tomorrow as pronouns (specifically, deictic temporal pronouns). Related info is in CGEL pages 429, 564-5.
Two other options (in addition to "as from today," "from today," and "effective today") are "beginning today" and "as of today." These may be more U.S.-idiomatic forms than British-idiomatic forms (the two "from" options have a British English sound to me, although "effective today" does not); but all five options are grammatically faultless, I believe.
The phrase our today's meeting is commonly used in Indian English, even though other dialects of English frown upon it. The mentioned examples in the comments of our today's specials and our today's speaker will, I think, sound off to many speakers, but possibly not as much as our today's meeting.
Why is "our today's meeting" wrong? - English Language & Usage Stack ...
Question: What are the origins and history of using on tomorrow, on today, and on yesterday ** (which in standard Englishes are just tomorrow, today, and yesterday)? Examples: US Journal of the Senate (2006, all bold font added): ORDERS FOR ADJOURNMENT UNTIL 9 A.M. ON TOMORROW ...
american english - Origins and history of "on tomorrow", "on today ...