The Spaniard had bossed the Grand Prix after starting from pole at the Northamptonshire circuit which had finally dried out after a week of torrential rain, with the track staying dry for the duration of the race.
But his soft tyres on the final stint were no match for Webber's hard compound, and he could not defend his lead as the Australian came through to win.
Championship leader Alonso still had enough of a cushion to fend off the Australian's Red Bull team-mate Sebastian Vettel, who took third.
Felipe Massa had his best race of the season to date as he finished fourth, ahead of Kimi Raikkonen in the Lotus.
Romain Grosjean showed remarkable pace to recover from an early clash with Paul di Resta which forced the Force India driver to retire, finishing sixth.
Michael Schumacher's recent resurgence continued as he took seventh ahead of a frustrated Lewis Hamilton, while Bruno Senna and Jenson Button rounded out the top 10.
It was a miserable day for McLaren, who looked short of pace throughout. Their points haul at Silverstone sees them slip down to fourth in the constructors' championship, behind Lotus and Ferrari, who both looked considerably faster.
With no dry running to speak of during the practice sessions, there was some doubt over the best tyre and pit stop strategies to run, but in the event the prime hard tyres proved more effective than the soft option compounds.
And the drivers who left their soft tyres until later, such as Alonso, Hamilton and Button, went on to struggle.
It looked like plain sailing for Alonso for most of the race, however, having scythed across Webber and into the first corner first.
In an eventful opening Di Resta's race came to a premature halt, while Massa leapfrogged Vettel and jousted with Schumacher for the final podium position.
Vettel's race was put back on track when Red Bull called an early first pit stop, which got him ahead of both men.
Behind him, Sergio Perez and Pastor Maldonado tangled just a few corners after pitting at the same time. It ended the Mexican's race, and effectively ruined the Venezuelan's, with Perez pointing the finger squarely at Maldonado afterwards.
Hamilton, running a longer opening stint, briefly took the lead as others pitted, but dropped back thereafter and scarcely made an impact thereafter.
Grosjean and Schumacher passed him with minimal fuss in the closing stages.
But the real drama was at the front. Alonso's four-second advantage over Webber with 14 laps remaining suddenly started to look fragile, and it became a matter of if and not when the Australian would pass.
The move came on lap 48, a superb DRS-assisted attack around the outside at the Loop. Once he had made it, a second win of the season, and his second triumph at Silverstone in three years, duly followed.