Hamilton's victory completes a hat trick of consecutive home wins at the British GP for the Mercedes driver, and is his fourth win on home soil and 47th F1 career victory.
Was there a Grand Prix on as well?
The win for Hamilton - even with Rosberg in second - but Hamilton just four points behind in the drivers championship.
"The Mercedes AMG Petronas Formula One Team today chose to withdraw its notice of intention to appeal against the decision of the Stewards of the British Grand Prix", a statement from Mercedes read.
El británico Lewis Hamilton conduce su Mercedes para ganar el Gran Premio de Gran Bretaña de la Fórmula Uno en el circuito de Silverstone, Inglaterra, el domingo 10 de julio de 2016.
Red Bull's Daniel Ricciardo said he was caught out by the timing of the Virtual Safety Car after finishing fourth at what he called a "boring" British Grand Prix.
In the pit lane, there were two near collisions before the race resumed and settled with Hamilton pulling 3.6 seconds clear by lap seven.
Mercedes, who had advised Rosberg to avoid seventh gear because his car's gearbox was failing, said they meant to appeal. "It's just insane to think that I'm up there with him", said Hamilton.
And Wolff was positively gushing as he saw Hamilton win by nearly seven seconds from Rosberg with 18-year-old Max Verstappen third before being promoted a place.
Eighth place would go to Carlos Sainz Jr, while Sebastian Vettel had a forgettable weekend to finish ninth, and Daniil Kvyat took home tenth place. Sixth-placed Toro Rosso now have 41 points. That, however, was great compared to the boos Rosberg got.
Hamilton once trailed Rosberg by 43 points after hard start to the campaign and said of his current gap to his team-mate: "That's kind of insane, it's been tough".
The German, who had a race-long battle with Verstappen, suffered a gearbox malfunction late in the 52-lap race at Silverstone. Apparently they gave him a few too many instructions, for the stewards would later deem that the team was in violation of the radio communication regulations. Indeed he spent much of the race in third after Verstappen pulled off a miraculous move around the outside of the German at Chapel.