"I've been waiting for this," shouted Briton Hamilton after crossing the line in his Mercedes to claim a ninth victory at Silverstone, breaking a tie with Michael Schumacher for most wins at one track.
Lando Norris of McLaren was third.
After his record-extending 104th Formula One victory, the 39-year-old Hamilton wept as he fell into the arms of his father as the home crowd roared.
"Since 2021, every day fighting, training and putting my mind to the task, working as hard as I can," Hamilton, who will be moving to Ferrari after this season, said at the finish line.
"This is my last race for the team here, I love them so much, I'll be forever grateful to everyone at Mercedes and to the incredible fans."
Hamilton, who started second on the grid behind his teammate George Russell, recorded his 13th consecutive podium at his home track.
Russell, the winner a week earlier in Austria, was forced out with a hydraulic problem.
Hamilton overtook Russell on lap 18 but was passed by Norris two laps later.
But a poorly executed McLaren pit stop allowed Hamilton to regain the lead with 12 laps remaining.
Hamilton finished 1.465sec ahead of Verstappen who overtook Norris three laps from the finish as the race ended in sunshine after a brief shower during the race.
Red Bull's Verstappen increased his lead in the drivers' standings over Norris by three points to 84 points despite failing to win for two consecutive races for the first time since Silverstone and Austria in 2022.
Oscar Piastri of McLaren was fourth with Carlos Sainz of Ferrari fifth and Nico Hulkenberg of Haas sixth.
