Dogs will chase the electronic hare round the 475m track at Walthamstow in London's East End for the last time this weekend.
An 11th hour attempt by a consortium to buy or lease the stadium ended in failure.
The stadium was opened by bookmaker William Chandler in 1933 and has remained in the Chandler family ever since.
But the owners say falling attendances and profits have made operations unsustainable.
Beckham, the former Manchester United player and England captain who now plays for LA Galaxy, and who was born in nearby Leytonstone, said: "I always remember my time working at Walthamstow dogs.
"I picked up glasses at the track.
"It was my first job and I was so happy to be getting a wage for the first time. It's a real shame to see it go as it means so much to the area. "
Walthamstow Labour MP Neil Gerrard said the closure would mean the loss of more than 400 part-time and full-time jobs.
