I would recommend treating the picture as an overlay.
So you would start the environment as
\begin{tikzpicture}[remember picture,overlay]
Even with this, the tikzpicture will have its origin (0,0) at the point where the picture is defined. So, I would recommend using relative coordinates and redefining where you want your origin with respect to the page nodes that TikZ provides. So here's something that might work for you:
\documentclass{article}
\usepackage{tikz}
\usepackage{geometry}
\geometry{
papersize={254mm,190.5mm},
margin = 0mm
}
\begin{document}
\noindent
\begin{tikzpicture}[remember picture,overlay]
\draw[line width=4pt,orange] (current page.south west) rectangle (current page.north east);
\path (current page.north west) -- ++ (0mm,-40mm) coordinate (origin);
\draw [->] (origin) to ++(10mm,10mm);
\draw [gray] (origin) rectangle ++(40mm,40mm);
\end{tikzpicture}%%
Hello (flush left) \hspace*{\fill} (flush right) Bye%%
\end{document}
which results in

Playing with where you place \noindent (such as immediately before Hello) will show you how the tikzpicture is being placed on the page.
If the tikzpicture is all that you're going to create with your document, you might want to consider using the standalone package.
\documentclass[border=2pt]{standalone}
%% I like a "border", but that's optional!
\usepackage{tikz}
\begin{document}
\noindent
\begin{tikzpicture}
\useasboundingbox (0,0) rectangle (254mm,190.5mm);
\coordinate (origin) at (0,0);
\draw [->] (origin) to ++(10mm,10mm);
\draw [gray] (origin) rectangle ++(40mm,40mm);
\end{tikzpicture}%%
\end{document}
Notice how I did not make this an overlay in this case. The above code results in

If you have other content for your document, either of these approaches can work.
Assuming that you want no other content on the same page as the tikzpicture, in the first approach you will have to issue something like
\clearpage
after the environment. And by using an overlay, you can use a page geometry more nature for your exposition.
Working with the second approach, you'll want to do something with \includegraphics and \raisebox to place it appropriately on the page.
If you provided more information about what kind of content you want in the picture, then I could probably give you better feedback.
tikzpictureas an overlay. So pass the environment the following in its optional arguments,remember picture,overlay– A.Ellett Jan 28 '16 at 17:15