Expand a Gantt chart automatically to textwidth of a page

Use the calc package to set the length as you need. Since the number of timeslots needs to be set manually in the \ganttitle command, I've created a ganttchart style timeslots which takes as its arguments the number of slots for the chart, and the text of the longest \gantttitle label (comma separated) and then uses that to calculate the width. It also sets the value of a macro \timeslots which can then be used in the \gantttitle command.

I've added the code as a ganttchart style, so that it can be specified without its own macro as in the previous version (see edit history for details). I've also added a length for the width that you want the autosizing to be relative to. For your specific example, it's set to \textwidth, but this allows you to set it to any width you like.

Usage: [ ..., timeslots={<number>,<text of longest label>}, ... ]

\usepackage[]{geometry} % show page borders
\parindent=0pt
\usepackage{pgfgantt}
\usepackage{calc}
\newlength{\myunitx}
\newlength{\autosizewidth}
\setlength{\autosizewidth}{\textwidth} % this allows you to change the value for autosizing
\newcommand*{\timeslots}{}
\ganttset{
timeslots/.code args={#1,#2}{\setlength{\myunitx}{(\autosizewidth-\widthof{#2}-1em)/#1}
                 \renewcommand{\timeslots}{#1}\pgfkeys{pgfgantt/x unit=\myunitx}}
}
\begin{document}

\begin{ganttchart}
    [
        timeslots={122,Long Long},  % timeslots
        time slot format=isodate    % Datumsformat
    ]
    {2017-04-01}{2017-07-31}        % from-to (122 days)

    \gantttitle{Gantt-Chart with 122 timeslots}{\timeslots}\\
    \ganttbar{Short}{2017-05-01}{2017-06-01}\\
    \ganttbar{Long Long}{2017-05-25}{2017-06-04}\\
    \end{ganttchart}

\begin{ganttchart}
    [
        timeslots={15,Foo},         % timeslots
        time slot format=isodate    % Datumsformat
    ]
    {2017-04-01}{2017-04-15}        % from-to (122 days)
    \gantttitle{Gantt-Chart with 15 timeslots}{15}\\
    \ganttbar{Foo}{2017-05-25}{2017-06-04}
\end{ganttchart}
\end{document}

Following discussion in chat, this is an adaption of Alan's answer which implements the syntax he was trying to realise.

% addaswyd o ateb Alan Munn: https://tex.stackexchange.com/questions/364944/expand-a-gantt-chart-automatically-to-textwidth-of-a-page/364969#364969 a chwestiwn buhtz: https://tex.stackexchange.com/questions/364944/expand-a-gantt-chart-automatically-to-textwidth-of-a-page
\documentclass[a4paper]{article}
\usepackage[showframe]{geometry} % show page borders
\parindent=0pt
\usepackage{pgfgantt}
\makeatletter
\tikzset{%
  /pgfgantt/time slots/.code={%
    \tikzset{%
      /pgfgantt/time slots/.cd,
      #1,
      /pgfgantt/.cd,
    }%
  },
  /pgfgantt/time slots/.search also={/pgfgantt},
  /pgfgantt/time slots/.cd,
  width/.store in=\ts@width,
  width=\textwidth,
  slots/.store in=\totaltimeslots,
  slots=20,
  label width/.store in=\ts@labelwidth,
  label width=25mm,
  calc x unit/.code n args=3{%
    \pgfmathsetmacro\ts@xunit{(#1-#2-0.6667em-2*\pgflinewidth)/#3}%
    \tikzset{%
      /pgfgantt/x unit=\ts@xunit pt,
    }%
  },
  widest/.code={%
    \pgfmathsetmacro\ts@wdlabel{width("#1")}%
    \tikzset{/pgfgantt/time slots/label width=\ts@wdlabel pt}%
  },
  calc x unit aux width/.style={/pgfgantt/time slots/calc x unit={#1}{\ts@labelwidth}{\totaltimeslots}},
  calc x unit aux label width/.style={/pgfgantt/time slots/calc x unit={\ts@width}{#1}{\totaltimeslots}},
  calc x unit aux slots/.style={/pgfgantt/time slots/calc x unit={\ts@width}{\ts@labelwidth}{#1}},
  width/.forward to=/pgfgantt/time slots/calc x unit aux width,
  slots/.forward to=/pgfgantt/time slots/calc x unit aux slots,
  label width/.forward to=/pgfgantt/time slots/calc x unit aux label width,
}
\makeatother
\begin{document}
\begin{ganttchart}
    [
        time slots={slots=122, widest=Long Long},
        time slot format=isodate,
    ]
    {2017-04-01}{2017-07-31}        % from-to (122 days)

    \gantttitle{Gantt-Chart with 122 timeslots}{\totaltimeslots}\\
    \ganttbar{Short}{2017-05-01}{2017-06-01}\\
    \ganttbar{Long Long}{2017-05-25}{2017-06-04}\\
\end{ganttchart}

\begin{ganttchart}
    [
        time slots/slots=15,
        time slots/widest=Foo,
        time slots/width=.9\linewidth,
        time slot format=isodate,
    ]
    {2017-04-01}{2017-04-15}        % from-to (122 days)
    \gantttitle{Gantt-Chart with 15 timeslots}{15}\\
    \ganttbar{Foo}{2017-05-25}{2017-06-04}
\end{ganttchart}
\end{document}