Kevin Carroll, who is also a senior figure in the nationalist British Freedom Party, will run in the anti-Islamic group's stronghold of Bedfordshire.
He is promising to end political correctness in policing and what he believes is a "two-tier" system that treats Muslims better than the rest of society.
If Mr Carroll won the election later this year, in addition to a £70,000 salary he would be given the power to set law and order priorities and budgets in the multicultural county as well as hiring and firing Bedfordshire Police chief constables.
Senior officers have already warned that public apathy about the new role of Police and Crime Commissioner could let extremist candidates into power by the back door.
Groups such as the EDL - which claims only to oppose extremist Muslims but whose members have been linked to football hooligans and the far-right - will work hard to get their supporters to vote while much of the electorate is expected to stay away from the polls taking place in 41 police areas across England and Wales.
Olly Martins, Labour's PCC candidate in Bedfordshire, said: "The EDL thugs are about the least appropriate people to run for police commissioner."
Mr Carroll, who lives in the EDL's heartland of Luton, has a conviction for a public order offence after he and another man hurled abuse at Muslims who were protesting at a soldiers' homecoming parade.
But although Mr Carroll received a nine-month conditional discharge in 2010 and was ordered to pay £175 costs, this will not prevent him from standing as a Police and Crime Commissioner because it was not an imprisonable offence.
By contrast Simon Weston, the Falklands war hero who had intended to run for the newly created post, would have been barred because of a teenage conviction for being a passenger in a stolen car, for which he could have been jailed.
So far the EDL has raised a fifth of the £5,000 deposit needed to put its "co-leader" up as a candidate for the election on November 15th.
A spokesman for the group, whose marches and street protests have regularly descended into violence, said: "Our only intention is to show our support for the police."
He said it was "more than likely" that the EDL would put up other candidates elsewhere but claimed their chances of winning were "not that high".
The spokesman added: "When you live in a town like Luton, their community is treated with kid gloves and our community is treated with hard fists.
"The police's hands are tied behind their backs by political correctness and fear of being called racist."