Hamilton was joined on the podium by his Mercedes team-mate, who finished second - but due to a 10 second radio penalty, was forced to concede this position to Red Bull's Max Verstappen.
For Hamilton, this marked his third consecutive victory at Silverstone - and was his fourth overall, trailing only Jim Clark and Alain Prost in total wins at the British Grand Prix.
The reigning world champion led the race from start to finish - but the race was anything but routine, as rain caused the race to begin behind a safety car.
The weather was a major factor in the race - as it caused teams to adjust their tyre strategy to attempt to make up ground on a wet track.
When the safety car came into the pits on the sixth lap - most teams opted to change tyres, but the Mercedes and Red Bull garages opted to stay on track and avoid the crowded pit lane.
After the dust had settled and all teams switched from wet weather tyres on to the intermediate compounds, Hamilton was the fastest on track and quickly opened up a 5 second gap ahead of the field.
As Hamilton drove into the distance - all eyes turned to Rosberg and Verstappen, who were engaged in a battle for second place.
Verstappen made the first major move - as the Dutch teenager bravely slipped away from the dry-line of the track to make an exquisite pass on Rosberg and jump into second place.
The wet weather got the best of a handful of drivers, including McLaren's Fernando Alonso and Toro Rosso's Carlos Sainz - who both caught a wet patches and saw their cars spin out in similar fashion before they re-joined the race.
Alonso and Sainz were not the only driver to lose controls and go for a spin, as six drivers did not finish the race, while many more slipped off the track and lost valuable positions.
As the race began to dry up, Rosberg was the fastest driver on track - and on Lap 38, he passed Verstappen for good and moved into second place and held on to this place until the end of the race as Mercedes completed a one-two, with Hamilton finishing almost seven seconds ahead of Rosberg to win the race.
However, this was short-lived - as it was deemed that Rosberg had breached race regulations when he received advice from the Mercedes garage about a gearbox issue, causing the German driver to be handed a ten second penalty.
Due to this penalty, Rosberg dropped one position on the grid behind Red Bull's Max Verstappen - who finished on the podium for the third time since his move from Toro Rosso earlier in the year.
Verstappen's Red Bull team-mate Daniel Ricciardo was the next driver to cross the line in fourth, while Ferrari's Kimi Raikkonen finished in fifth.
Force India's Sergio Perez and Nico Hulkenberg finishde in sixth and seventh respectively, while Toro Rosso's Carlos Sainz finished eighth.
Sebastian Vettel had a disappointing day and finished in ninth, after receiving a five-second penalty for pushing Felipe Massa off-track - while Daniil Kvyat was the last driver to score points in his Toro Rosso.