By winning, Hamilton joined Jim Clark and Alain Prost as the most successful driver on British soil - and has won at Silverstone for four consecutive years.
Hamilton was joined on the podium by his Mercedes team-mate Valtteri Bottas, while Kimi Raikkonen finished in third after a late tyre problem forced him to pit on the penultimate lap.
It was a dominant display from start to finish for Hamilton, who started the race on pole position - and on the first lap, he had already opened up a 1.6 second gap on his nearest competitor.
It appeared as though Hamilton was going to continue to pull away, but a crash between Toro Rosso teammates Daniil Kvyat and Carlos Sainz forced a safety car on the second lap - and also ended Sainz's race prematurely.
While this pulled the field back together, it was more of the same from Hamilton when the safety car left on Lap 5 - as the Mercedes driver pulled away yet again, leading from Raikkonen, while Verstappen, Vettel and Bottas closely followed.
As Hamilton roared away out front, there was a battle behind him for third place - as Verstappen and Vettel duked it out on Lap 14, with the Ferrari driver bumping his Dutch adversary off-track in an attempt to pass the Red Bull, but ultimately couldn't make it stick.
However, this battle was costly for the two - as they fell off the pace of the leaders, drifting to as much as 10 seconds behind Raikkonen in second place.
Eventually, Ferrari decided to yield and chose to bring Vettel into the pits on Lap 19 - looking for an opportunity to pass Verstappen with an undercut.
This gamble appeared to pay off for Ferrari when Verstappen came into the pits on the next lap - and exited behind Vettel, while Valtteri Bottas moved up to third after Mercedes opted to delay his pit-stop.
It was not all bad news for Red Bull, as Daniel Ricciardo rose through the field after starting the race in 19th - and at the halfway point of the race, Ricciardo had jumped 13 places into 6th.
As the laps ticked on, Hamilton started to extend his lead - and opened up a gap of 14 seconds on Raikkonen when Bottas finally made his pit-stop on Lap 33, switching to super soft tyres and exiting in front of Verstappen to slot into fourth.
After making his stop, Bottas was the fastest driver on track - and began to set his sights on a podium finish, slowly gaining on the Ferrari duo of Raikkonen and Vettel who sat in second and third respectively.
With eight laps remaining - Bottas made his move on Vettel, as he roared around the outside of the World Championship leader and into a podium position.
Second place looked out of reach for the Finnish driver, as he trailed his compatriot Raikkonen by over seven seconds with six laps to go - but he continued his pursuit and was gaining on the Ferrari.
On the penultimate lap, chaos ensued - as Raikkonen had troubles with his left-front tyre, forcing him to enter the pits and change tyres, dropping down to fourth and handing second place to Bottas, while Vettel climbed into a podium spot with one lap remaining.
But the drama continued when Vettel punctured his left-front tyre after Raikkonen re-emerged from the pits - handing the podium position right back to his team-mate, as the German crawled to the finish line with a puncture, choosing not to pit on the final lap.
As the chequered flag dropped, it was Lewis Hamilton who raced across the line first - finishing 14 seconds clear of his Mercedes teammate Valtteri Bottas, while Ferrari's Kimi Raikkonen averted a late disaster by finishing in third.
Max Verstappen finished fourth, but the young Dutch driver encountered some troubles of his own on the final lap - forcing him to make a quick stop into the pits on the penultimate lap, potentially costing him a spot on the podium in the process.
Daniel Ricciardo was the next driver to finish - a remarkable result given that he started the race in 19th position, rising 14 places to finish in fifth.
Renault's Nico Hulkenberg finished in sixth - passing Sebastian Vettel in the dying stages, as the Ferrari driver slowly crossed the line in seventh, narrowly clinging to his championship lead by a solitary point.
The Force India duo of Esteban Ocon and Sergio Perez finished in eighth and ninth respectively - while Williams' Felipe Massa rounded out the top ten.