scale column width with image width

It's unclear if you want to use overlays; if you don't, here's the definition of an environment that does the necessary computations. I add also a “less automatized” solution.

\documentclass{beamer}
\usepackage{mwe}

\newlength{\mycolwidth}
\newsavebox{\mycolwidthbox}
%% Better way
\newenvironment{picturecolumn}[2][]
 {\sbox\mycolwidthbox{\includegraphics[#1]{#2}}%
  \setlength{\mycolwidth}{\wd\mycolwidthbox}%
  \begin{columns}
  \begin{column}{\dimexpr\textwidth-\mycolwidth}
  \centering}
 {\end{column}
  \begin{column}{\mycolwidth}
  \usebox{\mycolwidthbox}
  \end{column}
  \end{columns}}

%% Simpler way
\newcommand{\setmycolwidth}[2][]{%
  \settowidth{\mycolwidth}{\includegraphics[#1]{#2}}%
}

\begin{document}
\begin{frame}

\begin{picturecolumn}[height=\dimexpr\paperheight-5pt]{example-image-golden-upright}
\centering
centered text\\
spanning multiple lines
\end{picturecolumn}
\end{frame}

\begin{frame}

\setmycolwidth[height=\paperheight]{example-image-golden-upright}

\begin{columns}
\begin{column}{\dimexpr\textwidth-\mycolwidth}
\centering
centered text\\
spanning multiple lines
\end{column}
\begin{column}{\mycolwidth}
\includegraphics[height=\paperheight]{example-image-golden-upright}
\end{column}
\end{columns}
\end{frame}

\end{document}

I hope I understood that right, that you want to get rid of the space right to the image, here is a solution involving parboxes.

\documentclass{beamer}
\usepackage{mwe}
\usepackage{calc}
%\usepackage{geometry} will be loaded with beamer
\newlength\rightcolumn
\begin{document}
\newgeometry{margin=0pt,includeall}
 \begin{frame}[plain]
 \settowidth{\rightcolumn}{\includegraphics[height=\paperheight]{example-image-golden-upright}}
   \parbox[t][\paperheight][c]{\paperwidth-\rightcolumn}{%
    \centering%
    centered text\\spanning multiple lines
   }%
   \parbox[t][\paperheight][c]{\rightcolumn}{%
    \includegraphics[height=\paperheight]{example-image-golden-upright}
   }%
 \end{frame}
\end{document}

And this results in: