Try this code:
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\tikzstyle{int}=[draw, fill=blue!20, minimum size=2em]
\tikzstyle{init} = [pin edge={to-,black}]
\begin{document}
\begin{tikzpicture}[node distance=4.5cm]
\node [int, pin={[init]below:Input1}] (a) {Box1};
\node (b) [left of=a, coordinate] {a};
\node [int, pin={[init]below:Input2}] (c) [right of=a] {Box2};
\node [coordinate] (end) [right of=c]{};
\path[->] (b) edge node[midway,above] {Arrow1} (a);
\path[->] (a) edge node[midway,above] {Arrow2} (c);
\draw[->] (c) edge node[midway,above] {Arrow3} (end) ;
\end{tikzpicture}
\end{document}
that produce this output:

EDIT1:
New code:
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\tikzstyle{int}=[draw, fill=blue!20, minimum size=2em]
\tikzstyle{init} = [pin edge={to-,black}]
\begin{document}
\begin{tikzpicture}[node distance=3.5cm]
\node [int, pin={[init]}] (a) {Input1};
\node (b) [left of=a, coordinate] {a};
\node [int, pin={[init]}] (c) [right of=a] {Input2};
\node [coordinate] (end) [right of=c]{};
\path[->] (b) edge node[midway,above] {Arrow1} (a);
\path[->] (a) edge node[midway,above] {Arrow2} (c);
\draw[->] (c) edge node[midway,above] {Arrow3} (end) ;
\end{tikzpicture}
\end{document}
New output:

EDIT2:
If you dont want arrows above the Input boxes try this code:
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\tikzstyle{int}=[draw, fill=blue!20, minimum size=2em]
\tikzstyle{init} = [pin edge={to-,black}]
\begin{document}
\begin{tikzpicture}[node distance=3.5cm]
% \node [int, pin={[init]}] (a) {Input1};
\node [int] (a) {Input1};
\node (b) [left of=a, coordinate] {a};
% \node [int, pin={[init]}] (c) [right of=a] {Input2};
\node [int] (c) [right of=a] {Input2};
\node [coordinate] (end) [right of=c]{};
\path[->] (b) edge node[midway,above] {Arrow1} (a);
\path[->] (a) edge node[midway,above] {Arrow2} (c);
\draw[->] (c) edge node[midway,above] {Arrow3} (end) ;
\end{tikzpicture}
\end{document}
that produce the output:
