Gilbert capped his fine late-season form with a convincing win in an enthralling 267-kilometre race in the Netherlands to take the first rainbow jersey of his career.
No-one could match the 30-year-old's pace after Gilbert put in a decisive dig on the eleventh and final ascent of the legendary Cauberg climb.
Norway's Boasson Hagen crossed the line in Valkenburg four seconds behind to take silver, while Spaniard Valverde completed the podium with a bronze-medal ride one second later.
"It's incredible. It hasn't sunk in yet. I've been dreaming of this for years," said Gilbert, winner of two stages in last month's Vuelta a Espana.
"To win in Valkenburg is amazing - it's so close to home and my wife is from the Netherlands.
"The team worked so hard and everyone did a really good job today. We definitely deserved to win the gold medal. I've won the Amstel Gold Race here twice so I knew I could do it today."
The win marks a remarkable turn-around for Gilbert, whose first season at BMC has been riddled with poor form, bad luck and sub-par performances. So dominant in the 2011 season, Gilbert did not pick up a win until his double scalp in Spain.
But Gilbert entered the world championships as the bookmakers' tip for the title - and he lived up to his billing as the best uphill sprinter in the peloton with yet another unbeatable ride.
Belgium controlled the race but things did not always go their way.
A break of eleven riders formed off the front of the peloton after 45 kilometres during the race's initial 100km undulating loop through the Dutch countryside. The break featured the likes of Pablo Lastras (Spain) and Dario Cataldo (Italy) and built up a maximum lead of four-and-a-half minutes before the riders hit the race's second phase, ten laps of a 16km circuit that featured both the Bemelerberg and Cauberg climbs.
Belgium did manage to get a man - Gianni Meersman - into a chasing group that formed on the Cauberg at the end of the second lap, around 130km from the finish.
The chasing group formed after an attack by Spain's Juan Antonio Flecha was foiled by Britain's Steve Cummings.
Britain had been very active in the early stages of the race, with reigning world champion Mark Cavendish and Tour de France winner Bradley Wiggins both riding hard on the front of the peloton.
Cavendish abandoned the race after the third lap while Olympic time trial champion Wiggins and Tour runner-up Chris Froome both threw in the towel after five laps.
Despite the presence of Meersman in the second break, Belgium led the pursuit of both leading groups, whittling down the advantage of the leaders to less than a minute towards the end of the fifth lap.
Vuelta a Espana winner Alberto Contador then put in a huge attack on the Cauberg, provoking a response by a cluster of riders - including Robert Gesink of the Netherlands, France's Thomas Voeckler and Britain's Jonathan Tiernan-Locke.
At the top of the climb, both leading groups and the Contador splinter group came together to form a break of 29 riders off the front of the peloton.
Belgium had another man - Bjorn Leukemans - inside the break alongside Meersman, but still it was the light blue jerseys of Belgium who led the chase.
The gap of the leading group grew to more than a minute with Spain's three riders combining well with Italy's four and France's three.
The Australian team of Simon Gerrans and the German team of John Degenkolb joined Belgium in setting the tempo on the front of the pack, which swept up the remaining escapees at the end of lap eight, 32km from the finish.
American Andrew Talansky attacked on the penultimate ascent of the Bemelerberg climb, provoking a reaction by Britain's Ian Stannard.
The unlikely duo carved out a lead of 15 seconds but were swept up on the Cauberg after Valverde combined with Tour of Britain winner Tiernan-Locke on the front of the pack.
Forty-eight riders remained in the leading pack as the race entered the final decisive lap. Spain looked strong with five riders near the front, including Contador, Valverde, Joaquim Rodriguez, Dani Moreno and Oscar Freire. Australia, too, looked poised with both Allan Davis and Simon Clarke working well for Milan-San Remo winner Gerrans.
Belgium kept their cool - and after Italy's Vincenzo Nibali made the first attack on the final climb of the Cauberg, 4km from the finish, it was Gilbert who replied with his decisive move.
Russia's Alexandr Kolobnev reacted the fastest, taking both Valverde and Boasson Hagen with him.
But Gilbert proved too strong and it quickly became a race for second place. Gilbert had time to ease up and savour his golden moment in the final few hundred metres of the flat run into the finish.
Boasson Hagen won the battle for second place ahead of Valverde, while Germany's Degenkolb - winner of five stages in the Vuelta - took fourth place ahead of Dutchman Lars Boom, Davis and Voeckler.
Three-time former world champion Freire took 10th place, two places ahead of Belgian Tom Boonen and four places ahead of the much-fancied Peter Sagan of Slovakia, who was unable to repeat his triple stage-winning Tour de France form.
An impressive Tiernan-Locke also finished in the main pack, five seconds in arrears, to take 19th place.