The following solution uses biblatex:
\documentclass{article}
\usepackage[
natbib=true,
style=authoryear,
labelnumber,
]{biblatex}
\addbibresource{references.bib}
\DeclareFieldFormat{labelnumberwidth}{[#1]}
\defbibenvironment{bibliography} % from numeric.bbx
{\list
{\printtext[labelnumberwidth]{%
\printfield{prefixnumber}%
\printfield{labelnumber}}}
{\setlength{\labelwidth}{\labelnumberwidth}%
\setlength{\leftmargin}{\labelwidth}%
\setlength{\labelsep}{\biblabelsep}%
\addtolength{\leftmargin}{\labelsep}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}%
\renewcommand*{\makelabel}[1]{\hss##1}}
{\endlist}
{\item}
\begin{filecontents}{references.bib}
@article{Smith:01,
author = {Smith, John},
year = {2001},
title = {Article title},
journal = {Journal title},
volume = {13},
pages = {1--2}
}
@book{Mueller:02,
author = {M{\"u}ller, Hans},
year = {2002},
title = {Book title},
publisher = {Publisher},
address = {Address}
}
\end{filecontents}
\begin{document}
\cite{Smith:01}, \cite{Mueller:02}
\printbibliography
\end{document}

Edit: Of course, if you're happy with the standard numeric style, there is an even simpler solution with biblatex, because one can make the difference between citestyle and bibstyle.
\documentclass{article}
\usepackage[
natbib=true,
citestyle=authoryear,
bibstyle=numeric,
]{biblatex}
\addbibresource{references.bib}
\begin{filecontents}{references.bib}
@article{Smith:01,
author = {Smith, John},
year = {2001},
title = {Article title},
journal = {Journal title},
volume = {13},
pages = {1--2}
}
@book{Mueller:02,
author = {M{\"u}ller, Hans},
year = {2002},
title = {Book title},
publisher = {Publisher},
address = {Address}
}
\end{filecontents}
\begin{document}
\cite{Smith:01}, \cite{Mueller:02}
\printbibliography
\end{document}
natbib? – Mico Jun 16 '15 at 22:41