Demolition contractor Griffiths McGee's first task was to bring down the control room, a glass and timber corridor between the twin towers that was built in 1966.
The towers themselves are expected to come down next month, and the Football Association plans to turn the rubble into mini-towers to sell as souvenirs, raising £1m in the process.
The England supporters' band evoked memories of last-minute goals and narrow victories by playing the theme from The Great Escape on the concourse while the demolition was in progress.
An England flag adorning the machinery was dwarfed by Multiplex banners on the stadium wall.
Multiplex director John Corcoran said: "Memories may stand the test of time, but bricks and mortar cannot always do the same. Now it's time to create another of the world's greatest stadiums more suited to modern needs."
Multiplex has 40 months to build the Foster and Partners-designed replacement.
Paul Gandy, managing director of Multiplex UK, said: "It's not just another construction project. I came to watch football here, and I remember the fantastic atmosphere – and the long queues for food."
The old stadium, built in 1923, lacked the catering facilities required in modern grounds. In contrast, the 90,000-seat replacement will include restaurant space for 10,000 spectators, including a banqueting hall that seats 2000.
A Brent council spokesperson said the scheme would create 4000 construction jobs as well as 10,000 services jobs for local people.
Wembley was confirmed as the location of the national stadium last week, after a £420m loan agreement between FA subsidiary Wembley National Stadium Limited and German bank WestLB was sealed.