I realise this question is already answered but I thought it might be worth mentioning an alternative solution using the fancyheadings package. While possibly overkill for this particular case, it provides flexible configuration of both headers and footers, and so has the potential to provide solutions to a range of variations on the theme of this question.
Headers and footers are here thought of as having 3 parts - left, centre and right. Odd and even headers/footers can be configured differently for two-sided documents, although it is also possible to simplify the configuration commands when things should be repeated. In addition, commands are provided to insert rules beneath headers or above footers. By default, a rule is provided beneath the header but no rule is drawn for footers. All of this is highly configurable, though.
For full details, you'd want to read the documentation. However, I've tried to indicate the basic options available by commenting the code which would answer the particular question asked here.
\documentclass[twoside]{report}
\usepackage{lipsum} %% dummy text
\usepackage{fancyhdr}
\pagestyle{fancy}
% unset defaults - no optional argument so this sets everything to empty
\fancyhf{}
\renewcommand{\headrulewidth}{0pt}
% set what you need
% reset the width of the header rule to the package default
% \renewcommand{\headrulewidth}{0.4pt}
% add a corresponding rule above footers
% \renewcommand{\footrulewidth}{0.4pt}
% \fancyhf[loh]{\fontsize{10}{12}\selectfont Left, odd header part}
\fancyhf[coh]{\fontsize{10}{12}\selectfont Centre, odd header part}
% \fancyhf[roh]{\fontsize{10}{12}\selectfont Right, odd header part}
% \fancyhf[leh]{\fontsize{10}{12}\selectfont Left, even header part}
\fancyhf[ceh]{\fontsize{10}{12}\selectfont Centre, even header part}
% \fancyhf[reh]{\fontsize{10}{12}\selectfont Right, even header part}
% \fancyhf[lof]{\fontsize{10}{12}\selectfont Left, odd footer part}
% \fancyhf[cof]{\fontsize{10}{12}\selectfont Centre, odd footer part}
% \fancyhf[rof]{\fontsize{10}{12}\selectfont Right, odd footer part}
% \fancyhf[lef]{\fontsize{10}{12}\selectfont Left, even footer part}
% \fancyhf[cef]{\fontsize{10}{12}\selectfont Centre, even footer part}
% \fancyhf[ref]{\fontsize{10}{12}\selectfont Right, even footer part}
% for single-sided or in case the same centre header is wanted for odd and even pages
% \fancyhf[ch]{\fontsize{10}{12}\selectfont Common central header part}
\begin{document}
\lipsum
\end{document}
This produces

\hfillbefore or after the text. – Sigur Dec 28 '13 at 12:29\hfillat both sides of the text did the trick. You can submit an answer and I will accept it :) – Patryk Dec 28 '13 at 12:52