Yes, that's a pretty big subject, I don't know of a single source that covers it, and certainly nothing close to it at the click of a mouse button.
Orders of Battle by Joslen gives the Divisional picture, plus Armd and Tank Brigades, throughout the war. It doesn't though cover Supply and Transport, Medical, Workshops or Misc units in Divs or Bdes (though a few get a mention when part of a Brigade Group). He has snapshots for Army Troops at three times, Jun44, Nov(?)44 and May45. Nothing though in terms of when a particular RA Regt arrived in theatre, and nothing on their allocation to Corps and Armies within 21 Army Group.
It can be bought as a download from MLRS books or in print from Naval & Military Press. It's also on Fold3 as part of their link with N&MP. And there are plenty of attempted transcriptions on the web.
The US standard is Stanton's Order of Battle. I've never seen a copy so can't comment. The US Army Divisional order of battle in the ETO is online via the USACMH site –
link
Same proviso, emphasis on Divs, though it does list non-Div attachments.
There is a decent ORBAT for First Canadian Army via a hyperwar transcription but again lacking arrival dates.
Gary