In a landmark ruling, Judge Paul Collins issued an injunction against the far-right group ordering it to comply with equality laws.
He said the party's current membership rules meant it was "likely to commit unlawful acts".
The 17-page judgment, delivered at the Central London County Court, found the BNP's clause that any members must agree to preserve the integrity of an "indigenous British" society was illegal and should be withdrawn.
It ordered the removal of the pledge to oppose immigration into the UK and maintain Britons as the "overwhelming majority" racial group.
As part of the injunction, the BNP will also have to abandon its "intimidatory" policy of sending officials to the homes of prospective new members.
Mr Griffin said tonight the BNP's membership had reopened despite the injunction.
The party leader claimed he had amended the constitution to comply with the law.
He said he had used his authority to alter the wording to remove the obligation on applicants to adhere to the principles of the party.
Mr Griffin said: "Section 4, which deals with the requirements for membership and includes the demand that members support all the principles of the party, is not protected.
"I have, therefore, with immediate effect changed the section 4 requirements, as I am entitled to do, to comply with the court order.
"What this means is that people can apply to join the BNP without having to endorse and support the principles of the party."
He said the amended version of the constitution would be published online within 30 days.
"Membership applications are therefore now open and the 7,000-strong backlog will be processed in the order in which they applied," Mr Griffin added.
A spokesman for the EHRC said: "We will be monitoring the situation.
"They need to ensure they comply with the terms of the court order fully otherwise they will be in contempt.
"If we believe they are in contempt of the court order and the membership is not genuinely accessible then we will consider what further regulatory action may be necessary."
This could include calling the BNP back to court or launching a fresh action, he added.
Judge Collins said the sanction would apply until a new constitution is produced.
"The membership list will have to be closed until then," he said. "The BNP is required to make sure their membership is fully apprised of the situation."
BNP leader Nick Griffin, who met with shouts of "Nazi scum" from protesters as he arrived at the hearing, said the ruling "opened a very dangerous door".
But the Equality and Human Rights Commission (EHRC), which brought the case, hailed it as "ground breaking".
"As a piece of litigation, it's ground breaking," said Robin Allen QC, who represented the EHRC.
"It's the first time this type of injunction has been applied to a political party."
The judgment found that, while not unlawful to hold discriminatory views, it is illegal to use them to control entry to a political party.
The BNP has until 4pm on Monday to post a message on its website informing its members of the ruling.
It will also have to pay court costs, with the EHRC claiming £60,000.
Susie Uppal, director of legal enforcement at the EHRC, said: "Political parties, like any other organisation, are obliged to respect the law and not discriminate against people who wish to become members.
"The BNP will now have to take the necessary steps to ensure it complies with the Race Relations Act."
Last month the BNP scrapped its whites-only policy in an attempt to avoid legal action.
And on Tuesday, it withdrew its policy of opposing the integration of different ethnic groups in British society, which effectively ruled out mixed race marriages.
The BNP denied allegations of discrimination and said it had a "waiting list" of black and Asian people and would welcome more applications from ethnic minorities.
Mr Griffin said: "It's opened a very dangerous door and it is a huge change to the unwritten constitution of Britain.
"They are claiming that they have been granted the right to interfere in what a party believes but the only people who have the right to judge are the electorate."
He described the ruling as "more than symbolic" and "utterly bizarre", adding: "It has given an organ of the state the power to interfere in the aims and objectives of any political party."
The judgment was a "devastating personal humiliation" for Mr Griffin, anti-BNP campaign group Searchlight said.
A spokesman said: "His desperate attempt to give the BNP a veneer of respectability in time for the general election has been torn to shreds.
"The BNP has been proven in court to be as racist and extremist as ever."
Asian millionaire Mo Chaudry, who threatened to join the party to "fight them from the inside", welcomed today's judgment.
"This was the only decision that could have been made today," he said.
He was described as a "troublemaker" by Mr Griffin, who insisted the businessman would remain barred from the party.
But Mr Chaudry, who is longer intending to apply for BNP membership, laughed off the suggestion, saying: "All I can say is that I think I've made my point."
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