The German started from pole position and never dropped out of the lead at his home race as he extended his lead at the top of the drivers' standings.
The Mercedes driver, who signed a contract extension with the team earlier this week, told Sky Sports News: "Wow, what a great day after so many great events for me this week! I came here hoping for a win and it worked out perfectly.
"My Silver Arrow was so dominant, thanks to the team for this fantastic car. I'm so happy for Mercedes, it was the first win for many many years in Germany."
The victory was Rosberg's fourth of the season.